Deck 11: Annuities, Stocks, and Bonds

Question 1

Estimate Li's future accumulation if his net worth grows at 5% and the mutual funds with stocks and bonds grow at 10% and 6%, respectively. ____________

Answer 1

Consider the three parts separately.
This is a compounding interest problem.
The following information is given, There are compounding periods.
The interest rate per compounding period is .
Look across the top of the Compound Interest Table for and down the side for periods to find 4.32194.
Recall the formula for finding Compound Amount, , or Using, , and in the formula above, That is, the maturity value of his net worth is .
Consider the balance in the mutual funds with stocks.
This is an annuity problem.
The following table is given, There are compounding periods.
The interest rate per compounding period is .
Look across the top of the Amount of an Annuity Table for and down the side for 30 periods to find 164.494.
Recall the formula for finding Compound Amount, Or, Using , and in the formula above, Therefore, the future value of the mutual funds with stocks is .
Consider the balance in the mutual funds with bonds.
This is an annuity problem.
The following information is given, There are compounding periods.
The interest rate per compounding period is .
Look across the top of the Amount of an Annuity Table for and down the side for 30 periods to find 79.058.
Recall the formula, Finding Compound Amount, Or, Using , and in the formula above, That is, the future value of the mutual funds with bonds is .
Finding the total future value by adding these numbers together, .
Therefore, the future value is .

Question 2

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
Rodriguez decides to contribute a total of 10% of his salary to his retirement plan. So, American River contributes 8% and he contributes a full 10% of his salary. Find the total annual contribution into the retirement plan. ____________

Answer 2

The employee has an annual salary of $42,000 and he wants to contribute 10% of his salary to retirement plan. Management also contribute with matching contributions with a limit of 8%. Accordingly, the management cannot contribute more than 8% of the employee salary.
Find out the total annual contribution into the retirement plan, the contribution of the employee as well as the contribution made by the management.
Contribution made by the employee is calculated below: Contribution made by the management Total contribution = Therefore, the total annual contribution into the retirement plan of the employee is $7,560.

Question 3

To help you review, the numbers in brackets show the section in which the topic was discussed.
Find the amounts of this annuities.

Answer 3

This is a problem of finding the amount of an annuity.
The following information is given, There are payment periods.
The interest rate per payment period is .
Look across the top of the Amount of an Annuity Table for 6% and down the side for 8 periods to find 9.89747.
Recall the formula for finding amount of an annuity, Or, Using , and in the formula above, Therefore, the amount of annuity is .

Question 4

Li is amazed that he will be able to accumulate over $600,000. However, he knows that inflation will increase his cost of living significantly in 30 years. He assumes 3% inflation and wants to find the income he needs at age 67 to have the same purchasing power as $40,000 today. ( Hint: Look at inflation in Section and use the compound interest table in Section.) ____________

Question 5

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
For planning purposes, Rodriguez assumes he will work at American River until he is 60 and believes he can earn 8% per year in a global stock fund. Assume the contributions continue at the same level as in Exercise 1 and estimate the future value. ____________
Rodriguez decides to contribute a total of 10% of his salary to his retirement plan. So, American River contributes 8% and he contributes a full 10% of his salary. Find the total annual contribution into the retirement plan. ____________

Question 6

To help you review, the numbers in brackets show the section in which the topic was discussed.
Find the amounts of this annuities.

Question 7

Li has read newspaper articles stating that Social Security benefits will be reduced in the years ahead. After some thought, he decides to be conservative and assume that Social Security will pay only the first $30,000 of the annual income he needs at age 67. Find the remaining income he will need beginning at age 67. ____________

Question 8

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
Assume that there are 486 faculty full-time faculty who have been at American River College for more than 8 years. If their average income is $62,940, find the annual payroll. ____________

Question 9

To help you review, the numbers in brackets show the section in which the topic was discussed.
Find the amounts of this annuities.

Question 10

Li decides to plan funding for his retirement for 20 years, from ages 67 to 87. If funds earn 8% compounded annually, find the present value of the annual income that he needs at 67 based on the income from part (c). ____________

Question 11

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
Based on the annual payroll in Exercise 3, estimate the annual contributions American River must make into retirement plans if all faculty contribute at least 8% of their salary into their own plans. ____________
Assume that there are 486 faculty full-time faculty who have been at American River College for more than 8 years. If their average income is $62,940, find the annual payroll. ____________

Question 12

To help you review, the numbers in brackets show the section in which the topic was discussed.
Find the amounts of this annuities.

Question 13

Will his expected savings fund his retirement? ____________

Question 14

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
Assume that a wealthy donor has agreed to give American River College $250,000 per year for the next 5 years. Find the present value of these gifts, assuming 6% per year. ____________

Question 15

James Rivera earned his degree in drafting at a community college and recently began his new career. He was happy to learn that his new employer will deposit $2500 into his 401(k) retirement account at the end of each year. Find the amount he will have accumulated in 15 years if funds earn 8% per year. ____________

Question 16

What could go wrong with his plans? ____________

Question 17

AMERICAN RIVER COLLEGE
www.arc.losrios.edu
Facts:
• 1955: Founded
• 2012: Over 36,000 students
• 2013: Over 52% ethnically not white
American River offers students a choice of more than 70 different majors of study, including biology, engineering, hospitality management, mortuary science, collision repair, business, and even fire technology. College personnel work closely with students to help them find financial aid. Amazingly, about one-half of the students at American River College receive some kind of financial aid.
Roman Rodriguez had 3 years of experience when he went to work in Human Resources at American River College at a salary of $42,000. He began work on his 30th birthday. The college matches his contributions to his retirement plan up to 8% of his salary.
American River has decided to build a new classroom building and will need $8,250,000 in 7 years. They decide to make contributions into a sinking fund at the end of each 6-month period. Find the payment needed if funds earn 5% per year. ____________

Question 18

James Rivera from Exercise 5 has also decided to invest $1000 at the end of each 6 months in an IRA that grows tax deferred. Find the amount he will have accumulated if he does this for 15 years and earns 6% compounded semiannually. ____________
James Rivera earned his degree in drafting at a community college and recently began his new career. He was happy to learn that his new employer will deposit $2500 into his 401(k) retirement account at the end of each year. Find the amount he will have accumulated in 15 years if funds earn 8% per year. ____________

Question 19

Find the present value of this annuities.

Question 20

Find the present value of this annuities.

Question 21

Find the present value of this annuities.

Question 22

Find the present value of this annuities.

Question 23

Betty Yowski borrows money for a new swimming pool and hot tub. She agrees to repay the note with a payment of $1200 per quarter for 6 years. Find the amount she must set aside today to satisfy this capital requirement in an investment earning 8% compounded quarterly. ____________

Question 24

Dan and Mary Foster just divorced. The divorce settlement included $650 a month payment to Dan for the 4 years until their son turns 18. Find the amount Mary must set aside today in an account earning 12, per year compounded monthly to satisfy this financial obligation.

Question 25

Find the amount of each payment into a sinking fund for the following.

Question 26

Find the amount of each payment into a sinking fund for the following.

Question 27

Find the amount of each payment into a sinking fund for the following.

Question 28

Find the amount of each payment into a sinking fund for the following.

Question 29

Solve the following application problems.
The owner of Hickory Bar-B-Que plans to open a new restaurant in 4 years at a cost of $200,000. Find the required semiannual payment into a sinking fund if funds are invested in an account earning 6% per year compounded semiannually. ____________

Question 30

Solve the following application problems.
Lupe Martinez will owe her retired mother $45,000 for a piece of land. Find the required quarterly payment into a sinking fund if Lupe pays it off in 4 years and the interest rate is 10% per year compounded quarterly. ____________

Question 31

Solve the following application problems.
George Jones purchases 200 shares of Exxon Mobil stock at $85.82 per share. Find (a) the total cost ____________and (b) the annual dividend if the dividend per share is $2.28. [ 11.4] ____________

Question 32

Solve the following application problems.
Belinda Deal purchases 25 IBM bonds that mature in 2021 at 95.1. They have a coupon rate of 4.2%. Find (a) the total cost if commissions are $1 per bond, ____________ (b) the annual interest, ____________and (c) the effective interest rate rounded to the nearest tenth. ____________

Question 33

Explain the following.

Question 34

Explain the following.

Question 35

Find the amount of this ordinary annuities rounded to the nearest cent. Find the total interest earned. (See Examples.)
Finding the Value of an Annuity and Interest Earned
Roman Rodriguez's employer will match his contributions into a retirement plan up to 5% of his $32,000 annual salary. In other words, the employer will put $1 into his retirement plan for every $1 Rodriguez puts into his retirement plan up to the limit. Find the future amount in 8 years if every quarter he contributes the maximum allowed assuming (a) funds earn 4% compounded quarterly and (b) funds earn 8% compounded quarterly. (c) Then find the difference between the two.
CASE IN POINT
SOLUTION
Salary per quater = $32,000 ÷ 4 = $8000
(a) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 1% and down the side for 32 periods to find 37.49407.
Amount = $800 × 37.49407 = $29,995.26 (rounded)
(b) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 2% and down the side for 32 periods to find 44.22703.
Amount = $800 × 44.22703 = $35,381.62 (rounded)
(c) Difference = $35,381.62 ? $30,295.21 = $5086.41
Finding the Amount of an Annuity and Interest Earned
At the birth of her grandson, Junella Smith commits to help pay for his college education. She decides to make deposits of $600 at the end of each 6 months into an account for 17 years. Find the amount of the annuity and the interest earned, assuming 6% compounded semiannually.
SOLUTION
Interest of is earned each semiannual period. There are 17 × 2 = 34 semiannual periods in 17 years. Find 3% across the top and 34 periods down the side of the table for 57.73018.
Amount = $600 × 57.73018 = $ 34,638.11
Interest = $34,638.11 ? ( 34 × $600) = $14,238.11 (rounded)
Smith knows that a college education will cost a lot more in 17 years than it does now, but she also knows that $34,638.11 will be of great help to her grandson.
Financial Calculator solution
In this example, payment ($600), interest rate per compounding period (3,), and number of compounding periods (34) are known. Future value is the unknown. Enter the payment as a negative number since it is an outflow of cash that Junella Smith pays each month. Finally, press the key to find the future value, which is a positive value since it will be an inflow of cash to her grandson.

Question 36

Find the amount of this ordinary annuities rounded to the nearest cent. Find the total interest earned. (See Examples.)
Finding the Value of an Annuity and Interest Earned
Roman Rodriguez's employer will match his contributions into a retirement plan up to 5% of his $32,000 annual salary. In other words, the employer will put $1 into his retirement plan for every $1 Rodriguez puts into his retirement plan up to the limit. Find the future amount in 8 years if every quarter he contributes the maximum allowed assuming (a) funds earn 4% compounded quarterly and (b) funds earn 8% compounded quarterly. (c) Then find the difference between the two.
CASE IN POINT
SOLUTION
Salary per quater = $32,000 ÷ 4 = $8000
(a) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 1% and down the side for 32 periods to find 37.49407.
Amount = $800 × 37.49407 = $29,995.26 (rounded)
(b) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 2% and down the side for 32 periods to find 44.22703.
Amount = $800 × 44.22703 = $35,381.62 (rounded)
(c) Difference = $35,381.62 ? $30,295.21 = $5086.41
Finding the Amount of an Annuity and Interest Earned
At the birth of her grandson, Junella Smith commits to help pay for his college education. She decides to make deposits of $600 at the end of each 6 months into an account for 17 years. Find the amount of the annuity and the interest earned, assuming 6% compounded semiannually.
SOLUTION
Interest of is earned each semiannual period. There are 17 × 2 = 34 semiannual periods in 17 years. Find 3% across the top and 34 periods down the side of the table for 57.73018.
Amount = $600 × 57.73018 = $ 34,638.11
Interest = $34,638.11 ? ( 34 × $600) = $14,238.11 (rounded)
Smith knows that a college education will cost a lot more in 17 years than it does now, but she also knows that $34,638.11 will be of great help to her grandson.
Financial Calculator solution
In this example, payment ($600), interest rate per compounding period (3,), and number of compounding periods (34) are known. Future value is the unknown. Enter the payment as a negative number since it is an outflow of cash that Junella Smith pays each month. Finally, press the key to find the future value, which is a positive value since it will be an inflow of cash to her grandson.

Question 37

Find the amount of this ordinary annuities rounded to the nearest cent. Find the total interest earned. (See Examples.)
Finding the Value of an Annuity and Interest Earned
Roman Rodriguez's employer will match his contributions into a retirement plan up to 5% of his $32,000 annual salary. In other words, the employer will put $1 into his retirement plan for every $1 Rodriguez puts into his retirement plan up to the limit. Find the future amount in 8 years if every quarter he contributes the maximum allowed assuming (a) funds earn 4% compounded quarterly and (b) funds earn 8% compounded quarterly. (c) Then find the difference between the two.
CASE IN POINT
SOLUTION
Salary per quater = $32,000 ÷ 4 = $8000
(a) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 1% and down the side for 32 periods to find 37.49407.
Amount = $800 × 37.49407 = $29,995.26 (rounded)
(b) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 2% and down the side for 32 periods to find 44.22703.
Amount = $800 × 44.22703 = $35,381.62 (rounded)
(c) Difference = $35,381.62 ? $30,295.21 = $5086.41
Finding the Amount of an Annuity and Interest Earned
At the birth of her grandson, Junella Smith commits to help pay for his college education. She decides to make deposits of $600 at the end of each 6 months into an account for 17 years. Find the amount of the annuity and the interest earned, assuming 6% compounded semiannually.
SOLUTION
Interest of is earned each semiannual period. There are 17 × 2 = 34 semiannual periods in 17 years. Find 3% across the top and 34 periods down the side of the table for 57.73018.
Amount = $600 × 57.73018 = $ 34,638.11
Interest = $34,638.11 ? ( 34 × $600) = $14,238.11 (rounded)
Smith knows that a college education will cost a lot more in 17 years than it does now, but she also knows that $34,638.11 will be of great help to her grandson.
Financial Calculator solution
In this example, payment ($600), interest rate per compounding period (3,), and number of compounding periods (34) are known. Future value is the unknown. Enter the payment as a negative number since it is an outflow of cash that Junella Smith pays each month. Finally, press the key to find the future value, which is a positive value since it will be an inflow of cash to her grandson.

Question 38

Find the amount of this ordinary annuities rounded to the nearest cent. Find the total interest earned. (See Examples.)
Finding the Value of an Annuity and Interest Earned
Roman Rodriguez's employer will match his contributions into a retirement plan up to 5% of his $32,000 annual salary. In other words, the employer will put $1 into his retirement plan for every $1 Rodriguez puts into his retirement plan up to the limit. Find the future amount in 8 years if every quarter he contributes the maximum allowed assuming (a) funds earn 4% compounded quarterly and (b) funds earn 8% compounded quarterly. (c) Then find the difference between the two.
CASE IN POINT
SOLUTION
Salary per quater = $32,000 ÷ 4 = $8000
(a) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 1% and down the side for 32 periods to find 37.49407.
Amount = $800 × 37.49407 = $29,995.26 (rounded)
(b) Interest of is earned per quarter for 8 × 4 = 32 quarters. Look across the top of the table for 2% and down the side for 32 periods to find 44.22703.
Amount = $800 × 44.22703 = $35,381.62 (rounded)
(c) Difference = $35,381.62 ? $30,295.21 = $5086.41
Finding the Amount of an Annuity and Interest Earned
At the birth of her grandson, Junella Smith commits to help pay for his college education. She decides to make deposits of $600 at the end of each 6 months into an account for 17 years. Find the amount of the annuity and the interest earned, assuming 6% compounded semiannually.
SOLUTION
Interest of is earned each semiannual period. There are 17 × 2 = 34 semiannual periods in 17 years. Find 3% across the top and 34 periods down the side of the table for 57.73018.
Amount = $600 × 57.73018 = $ 34,638.11
Interest = $34,638.11 ? ( 34 × $600) = $14,238.11 (rounded)
Smith knows that a college education will cost a lot more in 17 years than it does now, but she also knows that $34,638.11 will be of great help to her grandson.
Financial Calculator solution
In this example, payment ($600), interest rate per compounding period (3,), and number of compounding periods (34) are known. Future value is the unknown. Enter the payment as a negative number since it is an outflow of cash that Junella Smith pays each month. Finally, press the key to find the future value, which is a positive value since it will be an inflow of cash to her grandson.

Question 39

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 40

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 ( rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 41

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 42

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 43

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.) Explain the difference between an annuity and an annuity due.
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 44

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.) Describe the differences between an IRA, a 401(k), and a 403(b). (See Objective.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.
Note: Refer to Appendix B for calculator basics.

Question 45

Solve the following application problems.
SAVING FOR A HOME Jim and Betty Collins need an additional $6500 for a down payment on a home they hope to buy in 2 years. They invest $800 at the end of each quarter in an account earning 6% compounded quarterly. Find (a) the amount of the annuity ____________and (b) the interest earned. ____________

Question 46

Solve the following application problems.
CHILD-CARE PAYMENTS Monique Chaney places $250 of her quarterly child support check into an annuity for the education of her child. She does this at the beginning of each quarter for 8 years into an account paying 8% per year, compounded quarterly. Find (a) the amount of the annuity ____________and (b) the interest earned. ____________

Question 47

Solve the following application problems.
RETIREMENT Jason Horton works for Chevron as a welder on offshore drilling rigs. His retirement plan contributions are $3800 at the beginning of each 6-month period. Assume that the account grows at 6% compounded semiannually for 15 years. Find the (a) future value of the annuity ____________and (b) the interest earned. ____________

Question 48

Solve the following application problems.
MUTUAL FUND INVESTING Sandra Gonzales deposits $1000 into a mutual fund containing international stocks at the end of each semiannual period for 12 years. Assume the fund earns 10% interest compounded semiannually and find the future value. ____________

Question 49

Solve the following application problems.
T-BILL AND STOCK INVESTING Joann Gretz (see Example, page) decides to place half of her $2000 deposit at the end of each year into the bond fund and half into the stock fund. Assume the bond fund earns 6% compounded annually and the stock fund earns 10% compounded annually. Find the amount available in 33 years. ____________
Finding the Value of an IRA
At 27, Joann Gretz sets up an IRA with online broker Charles Schwab, where she plans to deposit $2000 at the end of each year until age 60. Find the amount of the annuity if she invests in (a) a bond fund that has historically yielded 6% compounded annually versus (b) a stock fund that has historically yielded 10% compounded annually. Assume that future yields equal historical yields.
SOLUTION
Age 60 is 60 ? 27 = 33 years away , so she will make deposits at the end of each year for 33 years.
(a) Bond fund: Look down the left column of the amount of an annuity table on page for 33 years and across the top for 6% to find 97.34316.
Amount = $2000 × 97.34316 = $194,686.32
(b) Stock fund: Look down the left column of the table for 33 years and across the top for 10, to find 222.25154.
Amount = $2000 × 222.25154 = $ 444,503.08
Quick TIP
Investments can be risky. For example, stocks usually increase in value over the long term, but they may go down as well.
The differences in the two investments are shown in the figure. Gretz wants the larger amount, but she is worried she might lose money in the stock fund. See Exercise 20 at the end of this section to find her investment choice.

Question 50

Find the present value of this annuities. Round to the nearest cent. (See Examples.)
Finding the Present Value of an Annuity
At the end of each quarter for 5 years, the Daily News deposits $4325 in an account paying 6% compounded quarterly. The goal is to accumulate funds for a new printing press. ( a ) Use the concepts of Section to find the future value of the annuity. ( b ) Then find the lump sum (present value) that must be deposited today to accumulate the same future value.
SOLUTION
(a) (or 1.5%) per quarter; 5 years × 4 = 20 quarters. Use the amount of an annuity table in Section to find 23.12367.
Future value = $4325 × 23.12367 = $ 100,009.87 (rounded)
(b) It is not necessary to use this future value to find the present value of the annuity. Instead, use the present value of an annuity table with 1.5, per period and 20 periods to find 17.16864.
Present value = $4325 × 17.16864 = $74,254.37
Thus, a deposit of $4325 at the end of every quarter for 5 years has a present value today of $74,254.37. If we assume 6% compounded quarterly and ignore income taxes, each of the following has exactly the same value:
1. 20 end-of-quarter deposits of $4325
2. A future value at the end of 5 years of $100,009.87
3. A present value on hand today of $74,254.37
Finding the Present Value
Tom and Brandy Barrett recently divorced. The judge gave custody of their 4-year-old son to Brandy and ruled that Tom must pay $1500 in child support to Brandy at the end of each quarter until the son turns 16. Find the lump sum that Tom must put into an account earning 6% compounded quarterly to cover the periodic payments. Find the interest earned.
SOLUTION
Payments must be made for 16 - 4 = 12 years, or for 12 × 4 = 48 quarters. The interest rate per quarter is per quarter. Look across the top of the present value of an annuity table for 1.5% and down the side for 48 payments to find 34.04255.
Present value of annuity = $1500 × 34.04255 = $ 51,063.83
A deposit of $51,063.83 today will make 48 end-of-quarter payments of $1500 each. Interest earned during the 12 years is the sum of all payments less the original lump sum.
Interest = (48 × $1500) - $51,063.83 = $20,936.17
Quick TIP
Although the $1500 withdrawals to Brandy are at the end of each quarter, the original lump sum must be deposited at the beginning of the first year.
Finding the Present Value
An American company hires a project manager to work in Saudi Arabia. The contract states that if the manager works there for 5 years, he will receive an extra benefit of $15,000 at the end of each semiannual period for the 8 years that follow. Find the lump sum that can be deposited today to satisfy the contract, assuming 6% compounded semiannually.
SOLUTION
The project manager works from years 1 to 5. He then receives two $15,000 annuity payments each year during years 6 through 13. Solve this problem in two steps.
1. Find the present value at the beginning of year 6 of the annuity with $15,000 payments.
Use per compounding period and 8 × 2 = 16 compounding periods to find 12.56110 in the present value of an annuity table.
Present value of annuity = $15,000 × 12.56110 = $188,416.50
This is the present value of the annuity needed at the beginning of year 6 to fund payments in years 6 through 13. But it is also the future value needed for the investment made today that will fund the eventual payments.
2. Find the lump sum needed today to accumulate the $188,416.50 by the end of year 5.
Use the table showing present value of a dollar in Section (page) with per compounding period and 5 × 2 = 10 compounding periods to find.74409.
Present value needed today = $188,416.50 ×.74409 = $ 140,198.83
A lump sum of $140,198.83 today will grow to $188,416.50 in 5 years. The $188,416.50 at the end of year 5 is enough to make 16 semiannual payments of $15,000 each during years 6 through 13.

Question 51

Find the present value of this annuities. Round to the nearest cent. (See Examples.)
Finding the Present Value of an Annuity
At the end of each quarter for 5 years, the Daily News deposits $4325 in an account paying 6% compounded quarterly. The goal is to accumulate funds for a new printing press. ( a ) Use the concepts of Section to find the future value of the annuity. ( b ) Then find the lump sum (present value) that must be deposited today to accumulate the same future value.
SOLUTION
(a) (or 1.5%) per quarter; 5 years × 4 = 20 quarters. Use the amount of an annuity table in Section to find 23.12367.
Future value = $4325 × 23.12367 = $ 100,009.87 (rounded)
(b) It is not necessary to use this future value to find the present value of the annuity. Instead, use the present value of an annuity table with 1.5, per period and 20 periods to find 17.16864.
Present value = $4325 × 17.16864 = $74,254.37
Thus, a deposit of $4325 at the end of every quarter for 5 years has a present value today of $74,254.37. If we assume 6% compounded quarterly and ignore income taxes, each of the following has exactly the same value:
1. 20 end-of-quarter deposits of $4325
2. A future value at the end of 5 years of $100,009.87
3. A present value on hand today of $74,254.37
Finding the Present Value
Tom and Brandy Barrett recently divorced. The judge gave custody of their 4-year-old son to Brandy and ruled that Tom must pay $1500 in child support to Brandy at the end of each quarter until the son turns 16. Find the lump sum that Tom must put into an account earning 6% compounded quarterly to cover the periodic payments. Find the interest earned.
SOLUTION
Payments must be made for 16 - 4 = 12 years, or for 12 × 4 = 48 quarters. The interest rate per quarter is per quarter. Look across the top of the present value of an annuity table for 1.5% and down the side for 48 payments to find 34.04255.
Present value of annuity = $1500 × 34.04255 = $ 51,063.83
A deposit of $51,063.83 today will make 48 end-of-quarter payments of $1500 each. Interest earned during the 12 years is the sum of all payments less the original lump sum.
Interest = (48 × $1500) - $51,063.83 = $20,936.17
Quick TIP
Although the $1500 withdrawals to Brandy are at the end of each quarter, the original lump sum must be deposited at the beginning of the first year.
Finding the Present Value
An American company hires a project manager to work in Saudi Arabia. The contract states that if the manager works there for 5 years, he will receive an extra benefit of $15,000 at the end of each semiannual period for the 8 years that follow. Find the lump sum that can be deposited today to satisfy the contract, assuming 6% compounded semiannually.
SOLUTION
The project manager works from years 1 to 5. He then receives two $15,000 annuity payments each year during years 6 through 13. Solve this problem in two steps.
1. Find the present value at the beginning of year 6 of the annuity with $15,000 payments.
Use per compounding period and 8 × 2 = 16 compounding periods to find 12.56110 in the present value of an annuity table.
Present value of annuity = $15,000 × 12.56110 = $188,416.50
This is the present value of the annuity needed at the beginning of year 6 to fund payments in years 6 through 13. But it is also the future value needed for the investment made today that will fund the eventual payments.
2. Find the lump sum needed today to accumulate the $188,416.50 by the end of year 5.
Use the table showing present value of a dollar in Section (page) with per compounding period and 5 × 2 = 10 compounding periods to find.74409.
Present value needed today = $188,416.50 ×.74409 = $ 140,198.83
A lump sum of $140,198.83 today will grow to $188,416.50 in 5 years. The $188,416.50 at the end of year 5 is enough to make 16 semiannual payments of $15,000 each during years 6 through 13.

Question 52

Find the present value of this annuities. Round to the nearest cent. (See Examples.)
Finding the Present Value of an Annuity
At the end of each quarter for 5 years, the Daily News deposits $4325 in an account paying 6% compounded quarterly. The goal is to accumulate funds for a new printing press. ( a ) Use the concepts of Section to find the future value of the annuity. ( b ) Then find the lump sum (present value) that must be deposited today to accumulate the same future value.
SOLUTION
(a) (or 1.5%) per quarter; 5 years × 4 = 20 quarters. Use the amount of an annuity table in Section to find 23.12367.
Future value = $4325 × 23.12367 = $ 100,009.87 (rounded)
(b) It is not necessary to use this future value to find the present value of the annuity. Instead, use the present value of an annuity table with 1.5, per period and 20 periods to find 17.16864.
Present value = $4325 × 17.16864 = $74,254.37
Thus, a deposit of $4325 at the end of every quarter for 5 years has a present value today of $74,254.37. If we assume 6% compounded quarterly and ignore income taxes, each of the following has exactly the same value:
1. 20 end-of-quarter deposits of $4325
2. A future value at the end of 5 years of $100,009.87
3. A present value on hand today of $74,254.37
Finding the Present Value
Tom and Brandy Barrett recently divorced. The judge gave custody of their 4-year-old son to Brandy and ruled that Tom must pay $1500 in child support to Brandy at the end of each quarter until the son turns 16. Find the lump sum that Tom must put into an account earning 6% compounded quarterly to cover the periodic payments. Find the interest earned.
SOLUTION
Payments must be made for 16 - 4 = 12 years, or for 12 × 4 = 48 quarters. The interest rate per quarter is per quarter. Look across the top of the present value of an annuity table for 1.5% and down the side for 48 payments to find 34.04255.
Present value of annuity = $1500 × 34.04255 = $ 51,063.83
A deposit of $51,063.83 today will make 48 end-of-quarter payments of $1500 each. Interest earned during the 12 years is the sum of all payments less the original lump sum.
Interest = (48 × $1500) - $51,063.83 = $20,936.17
Quick TIP
Although the $1500 withdrawals to Brandy are at the end of each quarter, the original lump sum must be deposited at the beginning of the first year.
Finding the Present Value
An American company hires a project manager to work in Saudi Arabia. The contract states that if the manager works there for 5 years, he will receive an extra benefit of $15,000 at the end of each semiannual period for the 8 years that follow. Find the lump sum that can be deposited today to satisfy the contract, assuming 6% compounded semiannually.
SOLUTION
The project manager works from years 1 to 5. He then receives two $15,000 annuity payments each year during years 6 through 13. Solve this problem in two steps.
1. Find the present value at the beginning of year 6 of the annuity with $15,000 payments.
Use per compounding period and 8 × 2 = 16 compounding periods to find 12.56110 in the present value of an annuity table.
Present value of annuity = $15,000 × 12.56110 = $188,416.50
This is the present value of the annuity needed at the beginning of year 6 to fund payments in years 6 through 13. But it is also the future value needed for the investment made today that will fund the eventual payments.
2. Find the lump sum needed today to accumulate the $188,416.50 by the end of year 5.
Use the table showing present value of a dollar in Section (page) with per compounding period and 5 × 2 = 10 compounding periods to find.74409.
Present value needed today = $188,416.50 ×.74409 = $ 140,198.83
A lump sum of $140,198.83 today will grow to $188,416.50 in 5 years. The $188,416.50 at the end of year 5 is enough to make 16 semiannual payments of $15,000 each during years 6 through 13.

Question 53

Find the present value of this annuities. Round to the nearest cent. (See Examples.)
Finding the Present Value of an Annuity
At the end of each quarter for 5 years, the Daily News deposits $4325 in an account paying 6% compounded quarterly. The goal is to accumulate funds for a new printing press. ( a ) Use the concepts of Section to find the future value of the annuity. ( b ) Then find the lump sum (present value) that must be deposited today to accumulate the same future value.
SOLUTION
(a) (or 1.5%) per quarter; 5 years × 4 = 20 quarters. Use the amount of an annuity table in Section to find 23.12367.
Future value = $4325 × 23.12367 = $ 100,009.87 (rounded)
(b) It is not necessary to use this future value to find the present value of the annuity. Instead, use the present value of an annuity table with 1.5, per period and 20 periods to find 17.16864.
Present value = $4325 × 17.16864 = $74,254.37
Thus, a deposit of $4325 at the end of every quarter for 5 years has a present value today of $74,254.37. If we assume 6% compounded quarterly and ignore income taxes, each of the following has exactly the same value:
1. 20 end-of-quarter deposits of $4325
2. A future value at the end of 5 years of $100,009.87
3. A present value on hand today of $74,254.37
Finding the Present Value
Tom and Brandy Barrett recently divorced. The judge gave custody of their 4-year-old son to Brandy and ruled that Tom must pay $1500 in child support to Brandy at the end of each quarter until the son turns 16. Find the lump sum that Tom must put into an account earning 6% compounded quarterly to cover the periodic payments. Find the interest earned.
SOLUTION
Payments must be made for 16 - 4 = 12 years, or for 12 × 4 = 48 quarters. The interest rate per quarter is per quarter. Look across the top of the present value of an annuity table for 1.5% and down the side for 48 payments to find 34.04255.
Present value of annuity = $1500 × 34.04255 = $ 51,063.83
A deposit of $51,063.83 today will make 48 end-of-quarter payments of $1500 each. Interest earned during the 12 years is the sum of all payments less the original lump sum.
Interest = (48 × $1500) - $51,063.83 = $20,936.17
Quick TIP
Although the $1500 withdrawals to Brandy are at the end of each quarter, the original lump sum must be deposited at the beginning of the first year.
Finding the Present Value
An American company hires a project manager to work in Saudi Arabia. The contract states that if the manager works there for 5 years, he will receive an extra benefit of $15,000 at the end of each semiannual period for the 8 years that follow. Find the lump sum that can be deposited today to satisfy the contract, assuming 6% compounded semiannually.
SOLUTION
The project manager works from years 1 to 5. He then receives two $15,000 annuity payments each year during years 6 through 13. Solve this problem in two steps.
1. Find the present value at the beginning of year 6 of the annuity with $15,000 payments.
Use per compounding period and 8 × 2 = 16 compounding periods to find 12.56110 in the present value of an annuity table.
Present value of annuity = $15,000 × 12.56110 = $188,416.50
This is the present value of the annuity needed at the beginning of year 6 to fund payments in years 6 through 13. But it is also the future value needed for the investment made today that will fund the eventual payments.
2. Find the lump sum needed today to accumulate the $188,416.50 by the end of year 5.
Use the table showing present value of a dollar in Section (page) with per compounding period and 5 × 2 = 10 compounding periods to find.74409.
Present value needed today = $188,416.50 ×.74409 = $ 140,198.83
A lump sum of $140,198.83 today will grow to $188,416.50 in 5 years. The $188,416.50 at the end of year 5 is enough to make 16 semiannual payments of $15,000 each during years 6 through 13.

Question 54

Explain the difference between the two ways to think of the present value of an annuity. (See Objective.)

Question 55

Explain the meaning of equivalent cash price. (See Objective.)

Question 56

Solve this application problems. Round to the nearest cent.
COMPUTER REPLACEMENT The community college where Roman Rodriguez works sets aside an annual payment of $35,000 per year for 5 years so it will have funds to replace the personal computers, servers, and printers in the computer labs when needed. Assuming 5% compounded annually, what lump sum deposited today would result in the same future value? ____________

Question 57

Solve this application problems. Round to the nearest cent.
COLLEGE EXPENSES In addition to his scholarship, Benjamin Wink needs $8000 every 6 months for living expenses and tuition at his university. As an engineering major, it will take 5 years to complete his degree. Assume funds earn 5% per year and find ( a ) the lump sum that must be deposited to meet this need ____________and ( b ) the interest earned. ____________

Question 58

Solve this application problems. Round to the nearest cent.
DISASTER RELIEF After a terrible cyclone in Bangladesh, an international disaster relief organization agreed to help support families in a small city who lost everything with a payment of $25,000 every quarter for 5 years. Find (a) the lump sum that must be deposited to meet this need ____________and (b) the interest earned assuming 6% per year, compounded quarterly. ____________

Question 59

Solve this application problems. Round to the nearest cent.
PAYING FOR COLLEGE Tom Potter estimates that his daughter's college needs, beginning in 8 years, will be $3600 at the end of each quarter for 4 years. (a) Find the total ____________ (b) amount needed in 8 years assuming 8% compounded quarterly. (b) Will he have enough money available in 8 years if he invests $700 at the end of each quarter for the next 8 years at 8% compounded quarterly? ____________

Question 60

Solve this application problems. Round to the nearest cent.
VAN PURCHASE In 4 years, Jennifer Videtto will need to purchase a delivery van for (a) her plumbing company. She estimates it will require a down payment of $10,000 with (b) payments of $950 per month for 36 months. (a) Find the total amount needed in 4 years assuming 12% compounded monthly. ____________ (b) Will she have enough if she invests $2200 at the end of every quarter for 4 years and earns 6% compounded quarterly? ____________

Question 61

Solve this application problems. Round to the nearest cent.
SELLING A RESTAURANT Anna Stanley has two offers for her pizza business. The first (a) offer is a cash payment of $85,000, and the second is a down payment of $25,000 with (b) payments of $3500 at the end of each quarter for 5 years. (a) Identify the better offer assuming 8% compounded quarterly. ____________ (b) Find the difference in the present values. ____________

Question 62

Solve this application problems. Round to the nearest cent.
GROCERY STORE Adolf Hegman has two offers for his Canadian grocery company. The first offer is a cash payment of $540,000, and the second is a down payment of $240,000 with payments of $65,000 at the end of each semiannual period for 4 years. (a) Identify the better offer assuming 10% compounded semiannually. ____________ (b) Find the difference in the present values. ____________

Question 63

Solve this application problems. Round to the nearest cent.
SOCIAL SECURITY Jessica Thames expects to receive $18,400 per year based on her deceased husband's contributions to Social Security. Assume that she receives payments for 14 years and a rate of 4% per year, and find the present value of this annuity. ____________

Question 64

Solve this application problems. Round to the nearest cent.
SOCIAL SECURITY Warren and Bernice White's combined Social Security payments add up to $35,400 per year. Assume payments for 20 years and a rate of 6% per year, and find the present value. ____________

Question 65

Solve this application problems. Round to the nearest cent.
For 6 years, Jessica Savage deposits $1000 at the end of each quarter into a mutual fund earning 8% per year compounded quarterly. Find (a) the future value ____________and (b) the interest. ____________

Question 66

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$8200, money earns 6% compounded semiannually, 5 years____________

Question 67

Solve this application problems. Round to the nearest cent.
Mr. and Mrs. Thompson deposit $2000 at the beginning of each year for 20 years into a retirement account earning 6% compounded annually. Find (a) the future value ____________and (b) the interest. ____________

Question 68

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$12,000, money earns 10% compounded semiannually, 3 years____________

Question 69

Solve this application problems. Round to the nearest cent.
Jaime Navarro deposits $1000 at the end of every 6 months into a Roth IRA for 8 years at 10% compounded semiannually. Find (a) the future value ____________and (b) the interest. ____________

Question 70

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$50,000, money earns 4% compounded quarterly, 5 years____________

Question 71

Solve this application problems. Round to the nearest cent.
Solectron needs to purchase new equipment for its production line in 3 years. The company has been advised to deposit $135,000 at the end of each quarter into an account that managers believe will yield 10% per year compounded quarterly. Find the lump sum that could be deposited today that will grow to the same future value. ____________

Question 72

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$32,000, money earns 6% compounded quarterly, 3 years____________

Question 73

Solve this application problems. Round to the nearest cent.
Abel Plumbing saves $12,000 at the end of every semiannual period in an account earning 6% compounded semiannually to replace several of its trucks in 5 years. Find the lump sum that could be deposited today that will grow to the same future value. ____________

Question 74

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$7894, money earns 12% compounded monthly, 3 years____________

Question 75

Solve this application problems. Round to the nearest cent.
Katherine Wysong was injured when she fell on ice at work. Her employer's workers compensation insurance paid for her medical bills and must also pay her $5000 per quarter for the next 6 years. Find the lump sum that must be deposited into an investment earning 4% per year compounded quarterly needed to make the payments. ____________

Question 76

Find the amount of the payment needed to accumulate the indicated amount in a sinking fund. Round to the nearest cent. (See Examples.)
Finding Periodic Payments
Administrators at a community college have decided to build, in 5 years, a new sports complex with two indoor 50-meter swimming pools and a large gymnasium. The cost estimate is $16,500,000. They decide to make end-of-quarter deposits into a fund expected to earn 6% compounded quarterly. Find ( a ) the amount of each quarterly payment and ( b ) the interest earned.
CASE IN POINT
SOLUTION
(a) Use per compounding period for 5 × 4 years = 20 compounding periods in the sinking fund table on page to find.04325.
Quarterly payment = $16,500,000 ×.04325 = $713,625
Twenty end-of-quarter payments of $713,625 at 6% compounded quarterly will grow to $16,501,629 using the table in Section.
(b) Interest is the future value minus the payments.
Interest = $16,501,629 ? 120 × $713,6252 = $ 2,229,129 (rounded)
Finding the Periodic Payments
First Christian Church sold $100,000 worth of bonds that must be paid off in 8 years. It now must set up a sinking fund to accumulate the necessary $100,000 to pay off the debt. Find the amount of each payment into a sinking fund if the payments are made at the end of each year and the fund earns 10% compounded annually. Find the amount of interest earned.
SOLUTION
Look along the top of the sinking fund table for 10% and down the side for 8 periods to find.08744.
Payment = $100,000 ×.08744 = $ 8744
The church must deposit $8744 at the end of each year for 8 years into an account paying 10% compounded annually to accumulate $100,000. The interest earned is the future value less all payments.
Interest = $100,000 ? (8 × $8744) = $ 30,048
Setting up a Sinking Fund Table
First Christian Church in Example deposited $8744 at the end of each year for 8 years into a sinking fund that earned 10% compounded annually. Set up a sinking fund table for these deposits. After each calculation, round each answer to the nearest cent before proceeding.
SOLUTION
The sinking fund account contains no money until the end of the first year, when a single deposit of $8744 is made. Since the deposit is made at the end of the year, no interest is earned.
At the end of the second year, the account contains the original $8744 plus the interest earned by this money. This interest is found by the formula for simple interest.
I = $8744 ×.10 × 1 = $874.40
An additional deposit is also made at the end of the second year, so that the sinking fund then contains the following total.
$8744 + $874.40 + $8744 = $18,362.40
Continue this work to get the following sinking fund table.
Quick TIP
Normally the last payment is adjusted as needed so that the future value exactly equals the desired amount. We assume this is true from this point forward.
$29,804, money earns 12% compounded monthly, 2 years____________

Question 77

Solve this application problems. Round to the nearest cent.
Carl and Amy Glaser recently divorced. As part of the divorce settlement, Carl must pay Amy $1000 at the end of every quarter for 8 years. Find the lump sum he must deposit into an account earning 8% per year compounded quarterly to make the payments. ____________

Question 78

Explain the difference between a sinking fund (see OBJECTIVE) and the present value of an annuity discussed in Section.

Question 79

Solve this application problems. Round to the nearest cent.
Ajax Coal sets up a sinking fund to purchase a new tractor in 3 years at a price of $870,000. Find the annual payment the firm must make if funds are deposited into an account earning 8% compounded annually. Then set up a sinking fund table.

Question 80

What is a sinking fund table? Who would use one? (See Objective.)