Deck 11: Ordinary Annuities: Periodic Payment, Number of Payments, and Interest Rate

Question 1

Calculate the amount that must be invested at the end of each year at 9% compounded annually in order to accumulate $500,000 after
a) 25 years.
b) 30 years.

Answer 1

a) $352,421.75
b) $389,954.60

Question 2

In order to accumulate $500,000 after 25 years, calculate the amounts that must be invested at the end of each year if the invested funds earn:
a. 6% compounded annually.
b. 7% compounded annually.
c. 8% compounded annually.
d. 9% compounded annually.
Also calculate the total earnings in each case. (Note that the total earnings increase proportionately more than the rate of return from one case to the next.)

Answer 2

a) $9113.86 & $272,166.00
b) $7905.26 & $302,368.50
c) $6839.39 & $329,015.25
d) $5903.13 & $352,421.75 $289,546.40
$9328.37 & $346,269.60

Question 3

A 20-year annuity is purchased for $400,000. What payment will it deliver at the end of each quarter if the undistributed funds earn:
a. 4% compounded quarterly?
b. 5% compounded quarterly?
c. 6% compounded quarterly?
d. 7% compounded quarterly?
In each case, also calculate the total earnings distributed over the life of the annuity. (Note that the total earnings increase proportionately more than the rate of return from one case to the next.)

Answer 3

a) $7287.54 & $183,003.20
b) $7938.61 & $235,088.80
c) $8619.33 & $66,861.80
d) $805.59 & $93,341.60

Question 4

The interest rate on a $100,000 loan is 7.5% compounded monthly. What must be the monthly payment for the loan to be repaid in:
a. 5 years?
b. 10 years?
c. 15 years?
d. 20 years?
Also calculate the total interest paid in each case. (Note that a doubling of the term more than doubles the total interest paid over the life of the loan.)

Question 5

Assume that the investments within an RRSP will earn 7% compounded annually. What monthly contribution must be made to the RRSP for it to grow to $750,000 in:
a. 15 years?
b. 20 years?
c. 25 years?
d. 30 years?
Also calculate the total earnings within the RRSP in each case. (Note that the total earnings increase proportionately more than the duration of contributions.)

Question 6

Marissa intends to make contributions to a TFSA such that the account will accumulate $150,000 after 20 years. What end-of-quarter contributions must be made if the TFSA earns 6% compounded:
a. annually?
b. semiannually?
c. quarterly?
d. monthly?

Question 7

What monthly payment is required to pay off a $50,000 loan in seven years if the interest rate on the loan is 7.5% compounded:
a. annually?
b. semiannually?
c. quarterly?
d. monthly?

Question 8

The first of 80 quarterly payments on a $50,000 loan at 6.4% compounded quarterly will be made 30 months after the date the loan was granted. What will be the amount of each payment?

Question 9

Noel has $300,000 with which to purchase an ordinary annuity delivering monthly payments after a 10-year period of deferral. What monthly payment will he receive if the undistributed funds earn 5% compounded semiannually?

Question 10

Henry can buy a farm for $700,000 with terms of $100,000 down and the balance payable over 20 years by quarterly payments including interest at 8% compounded annually. What will be the size of the payments? How much interest will Henry pay over the life of the loan?

Question 11

RBC Royal Bank approved a four-year $20,000 Royal Buy-Back Car Loan to Zaman at 7.5% compounded monthly. The monthly payments are to reduce the balance on the loan to the Royal Bank's guaranteed buy-back value of $7250. Calculate the monthly payment.

Question 12

In order to purchase another truck, Beatty Transport obtained a $50,000 term loan for 5 years at 7.8% compounded semiannually.
a) What are the monthly payments on the loan?
b) What will be the loan's balance at the end of the second year?
c) How much interest will Beatty pay in the first two years?

Question 13

Mr. Bean wants to borrow $7500 for three years. The interest rate is 9 % compounded monthly.
a) What quarterly payments are required on the loan?
b) What will be the balance owed on the loan at the start of the third year?

Question 14

Semiannual payments of $3874.48 are made on a $50,000 loan at 6.5% compounded semiannually. How long will it take to pay off the loan?

Question 15

The future value of an annuity consisting of end-of-year investments of $1658.87 earning 5.2% compounded annually is $100,000. How many annual investments were made?

Question 16

For $200,000, Jamal purchased an annuity that delivers end-of-quarter payments of $3341.74. If the undistributed funds earn 4.5% compounded quarterly, what is the term of the annuity?

Question 17

If money in a new TFSA earns 8.25% compounded monthly, how long will it take for the plan to reach $30,000 in value based on end-of-month contributions of $209.59?

Question 18

An endowment fund is set up with a donation of $100,000. If it earns 9% compounded monthly, for how long it will sustain end-of-month withdrawals of $1000? (Include the final smaller withdrawal.)

Question 19

Rounding up the number of contributions to the next integer, how long will it take an RRSP to surpass $100,000 if it takes in end-of-quarter contributions of $3000 and earns 6% compounded quarterly?

Question 20

For how long has William been making end-of-quarter contributions of $1200 to his RRSP if the RRSP has earned 8.75% compounded annually and is presently worth $74,385?

Question 21

Monthly payments of $315.49 are required on a $20,000 loan at 5.5% compounded quarterly. What is the term of the loan?

Question 22

How long will it take an RRSP to grow to $700,000 if it takes in month-end contributions of $1000 and it earns:
a. 6% compounded monthly?
b. 7% compounded monthly?
c. 8% compounded monthly?
d. 9% compounded monthly?
Round up the number of contributions to the next integer.

Question 23

How long will it take for monthly payments of $800 to repay a $100,000 loan if the interest rate on the loan is:
a. 6% compounded monthly?
b. 7% compounded monthly?
c. 8% compounded monthly?
d. 9% compounded monthly?

Question 24

How long will it take for monthly payments of $740 to repay a $100,000 loan if the interest rate on the loan is:
a. 7.5% compounded annually?
b. 7.5% compounded semiannually?
c. 7.5% compounded quarterly?
d. 7.5% compounded monthly?

Question 25

How long will it take an RESP to grow to $200,000 if the plan owner contributes $1000 at the end of each quarter and the plan earns:
a. 8% compounded monthly?
b. 8% compounded semiannually?
c. 8% compounded quarterly?
d. 8% compounded monthly?
Round up the number of contributions to the next integer before calculating the total time.

Question 26

If $300,000 is used to purchase an annuity earning 7.5% compounded monthly and paying $2500 at the end of each month, what will be the term of the annuity?

Question 27

How much longer will it take month-end RRSP contributions of $500 to accumulate $500,000 than month-end contributions of $550? Assume that the RRSP earns 7.5% compounded monthly. Round the time required in each case to the next higher month.

Question 28

Suppose that you contribute $400 per month to your RRSP. Rounding up to the nearest month, how much longer will it take for the RRSP's value to reach $500,000 if it earns 7.5% compounded annually than if it earns 7.5% compounded monthly?

Question 29

How much longer will it take monthly payments of $1000 to pay off a $100,000 loan if the monthly compounded rate of interest on the loan is 10.5% instead of 9.75%?

Question 30

Bonnie and Clyde want to take a six-month leave of absence from their jobs to travel extensively in South America. Rounded to the next higher month, how long will it take them to save $40,000 for the leave if they make month-end contributions of $700 to their employer's salary deferral plan? The salary deferral plan earns 7.5% compounded semiannually.

Question 31

Finest Furniture will sell a colour television set priced at $1395 for $50 down and payments of $50 per month, including interest at 13.5% compounded monthly. How long after the date of purchase will the final payment be made?

Question 32

$10,000 was invested in a fund earning 7.5% compounded monthly. How many monthly withdrawals can be made if the first occurs 3½ years after the date of the initial investment? Count the final smaller withdrawal.

Question 33

Twelve years ago, Mr. Lawton rolled a $17,000 retiring allowance into an RRSP that subsequently earned 10% compounded semiannually. Three years ago he transferred the funds to an RRIF. Since then, he has been withdrawing $1000 at the end of each quarter. If the RRIF earns 8% compounded quarterly, how much longer can the withdrawals continue?

Question 34

A property development company obtained a $2.5 million loan to construct a commercial building. The interest rate on the loan is 10% compounded semiannually. The lender granted a period of deferral until rental revenues become established. The first quarterly payment of $100,000 is required 21 months after the date of the loan. How long after the date of the original loan will the last payment be made?

Question 35

Harold's RRSP is already worth $56,000. Rounding to the next higher integer, how long will it take the RRSP to reach $250,000 if additional contributions of $2000 are made at the end of every six months? Assume the RRSP earns 9.75% compounded monthly.

Question 36

An annuity purchased for $50,000 sustained quarterly withdrawals of $1941.01 for 7 years and 9 months. What nominal rate of return and effective rate of return were the retained funds earning?

Question 37

The present value of an ordinary annuity of $500 per month for 8¾ years is $35,820. Calculate the nominal and effective values for the discount rate.

Question 38

If RRSP contributions of $3030.02 at the end of every six months are projected to generate a plan worth $500,000 in 25 years, what nominal and effective rates of return were assumed in the forecast?

Question 39

With end-of-month contributions of $251.33, a TFSA is expected to pass $100,000 in value after 15 years and 5 months. Determine the nominal and effective rates of return used in the projection.

Question 40

Monty is checking potential outcomes for the growth of his RRSP. He plans to make contributions of $500 at the end of each month. What nominal rate of return must his RRSP earn for its future value after 25 years to be:
a. $400,000?
b. $500,000?
c. $600,000?
(Note that a modest increase in the rate of return over a long period produces substantially larger future values.)

Question 41

Morgan has $500,000 accumulated in her RRSP and intends to use the amount to purchase a 20-year annuity. She is investigating the size of annuity payment she can expect to receive, depending on the rate of return earned by the undistributed funds. What nominal rate of return must the funds earn for the monthly payment to be:
a. $3000?
b. $3500?
c. $4000?

Question 42

An advertisement for Hyundai cars offered "2.9% 12-month financing or $1000 cash back." A car buyer financed $17,000 at the low interest rate instead of paying $16,000 cash (after the $1000 rebate). What was the effective rate of interest on the loan if the foregone cash rebate was treated as part of the cost of financing? (The 2.9% interest rate was a monthly compounded nominal annual rate.)

Question 43

Calculate the amount that must be invested at the end of every six months at 7.75% compounded semiannually in order to accumulate $500,000 after 20 years.

Question 44

If $400,000 accumulated in an RRSP is used to purchase an annuity earning 7.2% compounded monthly and paying $4500 at the end of each month, what will be the term of the annuity?

Question 45

The interest rate on a $30,000 loan is 7.5% compounded monthly.
a) What monthly payments are required to pay off the loan in eight years?
b) What monthly payments would be required to reduce the balance to $10,000 after five years?

Question 46

What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 8½ years from now will be $15,000?

Question 47

The McGowans are arranging a $90,000 mortgage loan from their bank. The interest rate on the loan will be 7.9% compounded semiannually.
a) What will the monthly payments be if the loan has a 20-year term?
b) If the McGowans choose to pay $800 per month, how long will it take to pay off the loan?

Question 48

Mr. Braun wants the value of his RRSP 25 years from now to have the purchasing power of $400,000 in current dollars.
a) Assuming an inflation rate of 4% per year, what nominal dollar amount should Mr. Braun have in his RRSP after 25 years?
b) What contributions should he make at the end of every three months to achieve the goal if his RRSP earns 7.5% compounded semiannually?

Question 49

A 70-year-old male can purchase either of the following annuities for the same price from a life insurance company. A 20-year-term annuity will pay $394 at each month-end. A life annuity will pay $440 at the end of each month until the death of the annuitant. Beyond what age must the man survive for the life annuity to have the greater economic value? Assume that money can earn 7.2% compounded monthly.

Question 50

Noreen's RRSP is currently worth $125,000. She plans to contribute for 10 more years and then let the plan continue to grow through internal earnings for an additional five years. If the RRSP earns 8% compounded annually, how much must she contribute at the end of every six months during the 10-year period to have $500,000 in the RRSP 15 years from now?

Question 51

Georgina is about to retire with $188,000 in her RRSP. She will make no further contributions to the plan, but will allow it to accumulate earnings for another five years. Then she will purchase an annuity providing payments of $6000 at the end of each quarter. What will be the annuity's term if the RRSP earns 8% compounded annually and the funds invested in the annuity earn 7.5% compounded monthly?

Question 52

By the time he turns 60, Justin (just turned age 31) wants the amount in his RRSP to have the purchasing power of $250,000 in current dollars. What annual contributions on his 32nd through 60^th birthdays inclusive are required to meet this goal if the RRSP earns 8% compounded annually and the rate of inflation is 2% per year?

Question 53

A life insurance company will sell a 20-year annuity paying $1600 at the end of each month for $175,000. What quarterly compounded nominal rate of interest will the annuitant earn?

A) 9.401%
B) 8.735%
C) 9.226%
D) 9.335%
E) 9.297%

Question 54

A $10,000 debt is repaid by payments of $800 at the end of each quarter for five years. What semiannually compounded nominal interest rate was charged on the loan?

A) 23.10%
B) 20.35%
C) 11.08%
D) 9.81%
E) 19.86%

Question 55

A $50,000 mortgage loan requires monthly payments of $520 for 20 years. What is the semiannually compounded nominal rate of interest on the loan?

A) 11.3752%
B) 11.6987%
C) 11.1146%
D) 0.9381%
E) 11.2573%

Question 56

What quarterly compounded rate of return will allow investments of $800 at the end of every six months to accumulate to $24,000 after 10 years?

A) 14.876%
B) 8.062%
C) 8.143%
D) 8.309%
E) 15.286%

Question 57

What regular investment, made at the end of every three months and earning 10% compounded quarterly, would accumulate to $475,000 in 20 years?

A) $3,492.86
B) $17,616.21
C) $7,856.83
D) $1,912.37
E) $7,916.67

Question 58

How much will Clarence have to invest at the end of every year at 11% compounded annually if he is going to accumulate $25,000 in five years?

A) $2,758.93
B) $3,870.52
C) $4,014.25
D) $4,989.01
E) $5,562.50

Question 59

The interest rate charged on a loan of $85,000 is 7.75% compounded annually. If the loan is to be paid off over seven years, calculate the size of the annual payments.

A) $13,084
B) $1,314
C) $9,599
D) $16,187
E) $17,492

Question 60

Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.

A) $983.75
B) $990.84
C) $998.00
D) $598.80
E) $716.44

Question 61

If you have $45,000 earning 9.6% compounded monthly, how much money could you take out of the investment at the end of every year for 10 years?

A) $8,820
B) $7,334
C) $2,819
D) $7,198
E) $2,878

Question 62

For the next 15 years Andre expects to earn 12% compounded monthly on the Retirement Savings Plan (RSP) that he is starting. For the subsequent 10 years he expects a return of 7% compounded annually. How much money is he planning to have in 25 years if he invests $3,500 at the end of every six months for the 25 years?

A) $411,922
B) $610,059
C) $382,600
D) $657,484
E) $1,068,912

Question 63

Clarence has been investing $1,000 at the end of every year at 11% compounded annually. With today's contribution his investment has grown to $44,500. How many years ago did he make the first contribution?

A) 26 years
B) 49 years
C) 16 years
D) 31 years
E) 12 years

Question 64

Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, Moses will, at the end of every six months, take $20,000 out of his Retirement Fund. For how long will he be able to do that before the money runs out?

A) 15.4 years
B) 35.0 years
C) 20.0 years
D) 12.9 years
E) 17.5 years

Question 65

The interest rate charged on an $85,000 loan is 7.75% compounded annually. How long will it take for the loan to be paid off by annual payments of $9,450?

A) 8 years
B) 12 years
C) 16 years
D) 20 years
E) 24 years

Question 66

If deposits of $9,900 invested at the end of every six months earn 13% compounded quarterly, how long will it take to accumulate $295,000?

A) 4.25 years
B) 8.5 years
C) 17.0 years
D) 34.0 years
E) 68.0 years

Question 67

You have $45,000 earning 9.6% compounded monthly. For how long will you be able to withdraw $5,000 at the end of every year?

A) 10.7 years
B) 13.9 years
C) 21.8 years
D) 24.4 years
E) 29.5 years

Question 68

Clarence has a retirement fund of $300,000 that earns 11% compounded quarterly. His plan is to withdraw $3,000 at the end of every month for 12 years and then increase the monthly withdrawals to $5,000. How many $5,000 withdrawals will he be able to make?

A) 30
B) 43
C) 48
D) 51
E) 56

Question 69

What would be the effective rate of interest if $100,000 was accumulated by investments of $3,500 made at the end of every three months for five years?

A) 15.20%
B) 14.40%
C) 8.65%
D) 13.12%
E) 34.61%

Question 70

A life insurance company advertises that $50,000 will purchase a 20-year annuity paying $402.80 at the end of each month. What effective rate of return does the annuity investment earn?

A) 6.15%
B) 6.92%
C) 7.76%
D) 7.18%
E) 7.50%

Question 71

A loan of $25,000,000 is to be repaid by annual year-end payments of $3,000,000 for 30 years. What is the effective interest rate on this loan?

A) 9.746%
B) 43.62%
C) 3.600%
D) 11.548%
E) 21.598%

Question 72

Susan's car loan payments are $265.08 at the end of each month for four years. The amount she borrowed was $12,000. What is the monthly compounded nominal interest rate?

A) 6.500%
B) 2.900%
C) 10.500%
D) 4.750%
E) 6.000%

Question 73

A lottery winner must decide between receiving $5,000 at the end of every month for 10 years or one lump sum of $1,000,000 after 10 years. What semi-annually compounded nominal rate of interest would make the two options equal in value?

A) 10.152%
B) 7.984%
C) 9.774%
D) 7.807%
E) 9.580%

Question 74

The Jacksons have agreed to pay $1,419 at the end of every month for 15 years on their mortgage loan of $167,000. What semi-annually compounded nominal rate are they paying?

A) 5.09%
B) 7.23%
C) 8.11%
D) 7.29%
E) 6.19%

Question 75

A loan of $88,700 can be paid off by monthly payments of $1,000 for 11 years. What is the semi-annually compounded nominal interest rate?

A) 9.81%
B) 6.45%
C) 7.74%
D) 7.86%
E) 8.02%

Question 76

Malcolm wants to purchase an annuity that will pay him $7,000 at the end of every three months for 15 years. His financial advisor has told Malcolm that this annuity will cost him $250,000. What monthly compounded nominal interest rate was used in this calculation?

A) 7.51%
B) 9.3%
C) 12.60%
D) 18.89%
E) 22.67%

Question 77

Sandy is planning to accumulate $500,000 after 30 years by making investments of $300 at the end of each month for 20 years and leaving the money to grow at 7% compounded semi-annually for 10 more years. What monthly compounded nominal rate will Sandy have to be earning over the 20 years that she makes the monthly deposits?

A) 8.96%
B) 10.75%
C) 11.30%
D) 12.83%
E) 7.12%

Question 78

A new car promotion offer 0.9% compounded monthly interest for the first 36 months on a loan of $57,000. The payments on this loan are $1,000 per month for five years. What annually compounded interest rate is being applied to the loan for the last two years?

A) 8.434%
B) 10.800%
C) 5.331%
D) 8.124%
E) 10.662%

Question 79

Calculate the periodic payment for the following ordinary annuity.

Question 80

Calculate the periodic payment for the following ordinary annuity.