Deck 5: Mathematics of Finance

Question 1

In the last 3 years, mutual fund A grew at the rate of 9.5%/year compounded quarterly. Over the same period, mutual fund B grew at the rate of 9.6%/year compounded semiannually. Which mutual fund has a better rate of return? ​

A) Fund A
B) Fund B

Answer 1

Fund A

Question 2

If the accumulated amount is $3,630 at the end of 3 years and the simple rate of interest is 7%/year, what is the principal? ​

A) The principal is $2,500.
B) The principal is $3,990.
C) The principal is $3,000.
D) The principal is $3,200.

Answer 2

The principal is $3,000.

Question 3

Find the present value of $30,000 due in 4 years at the given rate of interest 6%/year compounded monthly. ​

A) The present value is $23,741.10.
B) The present value is $23,255.83.
C) The present value is $23,612.95.
D) The present value is $22,941.71.

Answer 3

The present value is $23,612.95.

Question 4

Find the accumulated amount A if the principal P = $120,000 is invested at the interest rate of r = 6% per year for t = years compounded monthly. ​

A) The accumulated amount is $169,964.44.
B) The accumulated amount is $169,165.05.
C) The accumulated amount is $169,293.20.
D) The accumulated amount is $168,936.08.

Question 5

Find the accumulated amount A if the principal P = $10,000 is invested at the interest rate of r = 5% per year for t = 8.5 years, compounded quarterly. ​

A) The accumulated amount is $15,383.81.
B) The accumulated amount is $14,584.42.
C) The accumulated amount is $15,612.78.
D) The accumulated amount is $15,255.66.

Question 6

Find how much money should be deposited in a bank paying interest at the rate of 9.5%/year compounded quarterly so that at the end of 2 years the accumulated amount will be $30,000. ​

A) $24,864 should be deposited in a bank.
B) $30,265 should be deposited in a bank.
C) $33,628 should be deposited in a bank.
D) $28,391 should be deposited in a bank.

Question 7

A bank deposit paying simple interest at the rate of 4%/year grew to a sum of $1,900 in 11 months. Find the principal. Round your answers to nearest integer. ​

A) The principal is $1,812.
B) The principal is $1,889.
C) The principal is $1,896.
D) The principal is $4,400.
E) The principal is $1,833.

Question 8

Find the accumulated amount A if the priciple, P = $ is invested at the rate of r = %/year for t = years compounded daily. Round your answers to nearest integer. ​

A) The accumulated amount is $ .
B) The accumulated amount is $ .
C) The accumulated amount is $ .
D) The accumulated amount is $ .
E) The accumulated amount is $ .

Question 9

Find the simple interest on a $200 investment made for 5 years at an interest rate of 8%/year. What is the accumulated amount? ​

A) The simple interest is $80,
The accumulated amount is $280.
B) The simple interest is $105,
The accumulated amount is $255.
C) The simple interest is $100,
The accumulated amount is $300.
D) The simple interest is $95,
The accumulated amount is $265.

Question 10

A bank deposit paying simple interest grew from an initial sum of $1,000 to a sum of $1,045 in 9 mo. Find the interest rate. ​

A) The interest rate is 7%/year.
B) The interest rate is 6%/year.
C) The interest rate is 7.2%/year.
D) The interest rate is 5.5%/year.

Question 11

In order to help finance the purchase of a new house, the Abdullahs have decided to apply for a short-term loan (a bridge loan) in the amount of $120,000 for a term of 2 mo. If the bank charges simple interest at the rate of 14%/year, how much will the Abdullahs owe the bank at the end of the term? ​

A) $122,800
B) $240,000
C) $117,400
D) $126,300

Question 12

Find the effective rate corresponding to the given nominal rate 10% compounded semiannually. ​

A)
B)
C)
D)

Question 13

The Kwans are planning to buy a house 5 years from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 5%/year during that period. If this economic prediction holds true, how much can the Kwans expect to pay for a house that currently costs $170,000? ​

A) $208,204
B) $222,369
C) $220,495
D) $216,968

Question 14

Find the accumulated amount A if the principal P = $3,000 is invested at the interest rate of r = 6% per year for t = 4 years, compounded annually. ​

A) The accumulated amount is $3,116.19.
B) The accumulated amount is $3,430.31.
C) The accumulated amount is $3,787.43.
D) The accumulated amount is $3,915.58.

Question 15

Find the accumulated amount A if the principal, P = $ is invested at the interest rate r = %/year for t = years compounded semiannually. Round your answers to two decimal places. ​

A) The accumulated amount is $ .
B) The accumulated amount is $ .
C) The accumulated amount is $ .
D) The accumulated amount is $ .
E) The accumulated amount is $ .

Question 16

How many days will it take for a sum of $7,000 to earn $280 interest if it is deposited in a bank paying ordinary simple interest at the rate of 5%/year? (Use a 365-day year.) ​

A) It will take 472 days for a sum of $7,000 to earn $280.
B) It will take 242 days for a sum of $7,000 to earn $280.
C) It will take 292 days for a sum of $7,000 to earn $280.
D) It will take 272 days for a sum of $7,000 to earn $280.

Question 17

Mitchell has been given the option of either paying his $600 bill now or settling it for $612 after 1 mo. If he chooses to pay after 1 mo, find the simple interest rate at which he would be charged. ​

A) The simple interest rate is 0.25%/year.
B) The simple interest rate is 24%/year.
C) The simple interest rate is 25%/year.
D) The simple interest rate is 12%/year.

Question 18

Find the accumulated amount at the end of 6 months on an $400 deposit in the bank paying simple interest at the rate of 3% year. ​

A) The accumulated amount is $411.
B) The accumulated amount is $413.
C) The accumulated amount is $416.
D) The accumulated amount is $418.
E) The accumulated amount is $406.

Question 19

A young man is the beneficiary of a trust fund established for him 21 years ago at his birth. If the original amount placed in trust was $5,000, how much will he receive if the money has earned interest at the rate of 8%/year compounded annually? Compounded quarterly? Compounded monthly? ​

A) A young man will receive
$25,169 if the money has earned interest compounded annually,
$26,387 if the money has earned interest compounded quarterly,
$26,679 if the money has earned interest compounded monthly.
B) A young man will receive
$25,477 if the money has earned interest compounded annually,
$26,843 if the money has earned interest compounded quarterly,
$26,913 if the money has earned interest compounded monthly.
C) A young man will receive
$24,494 if the money has earned interest compounded annually,
$26,687 if the money has earned interest compounded quarterly,
$26,523 if the money has earned interest compounded monthly.
D) A young man will receive
$24,962 if the money has earned interest compounded annually,
$26,540 if the money has earned interest compounded quarterly,
$27,477 if the money has earned interest compounded monthly.

Question 20

Determine the simple interest rate at which $ will grow to $ in the months. Round your answers to the nearest tenth of percent. ​

A) The interest rate is %/year.
B) The interest rate is %/year.
C) The interest rate is %/year.
D) The interest rate is %/year.
E) The interest rate is %/year.

Question 21

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.81% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? ​

A) Investment A.
B) Investment B.

Question 22

Find the present value of $10,000 due in 3 years at the rate of interest 2%/year compounded quarterly. Round your answers to two decimal places. ​

A) The present value is $9,213.91.
B) The present value is $9,394.05.
C) The present value is $9,293.84.
D) The present value is $9,518.42.
E) The present value is $9,419.05.

Question 23

Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. ​

A) 7.44 %/yr
B) 7.32 %/yr
C) 6.39 %/yr
D) 8.01 %/yr
E) 7.78 %/yr

Question 24

Anthony invested a sum of money 4 yr ago in a savings account that has since paid interest at the rate of 8%/year compounded quarterly. His investment is now worth $20,591.80. How much did he originally invest? Please round the answer to the nearest cent. ​

A) $15,000.01
B) $14,500.01
C) $16,000.01
D) $13,500.01
E) $17,000.01

Question 25

Determine whether the statement is true or false. ​
Susan's salary increased from $40,000/year to $50,000/year over a 4-year period. Therefore, Susan got annual increases of 4% over that period.
​

A) True. This follows from formula A = P(1 + rt).
B) False. If Susan had gotten annual increases of 4 percent over 4 years, her salary would have been , or approximately $46,794.34 after 4 years, not $50,000.
​

Question 26

Find the present value of $30,000 due in 2 years at the given rate of interest 6%/year compounded monthly. Please round your answer to the nearest cent.
P = $ __________

Question 27

Mitchell has been given the option of either paying his $800 bill now or settling it for $814 after 1 mo. If he chooses to pay after 1 mo, find the simple interest rate at which he would be charged.
r = __________ %/year

Question 28

Today a typical family of four spends $600/month for food. If inflation occurs at the rate of 3%/year over the next 7 yr, how much should the typical family of four expect to spend for food 7 yr from now? Please round the answer to the nearest cent. ​

A) $739.43
B) $737.48
C) $767.99
D) $737.92
E) $710.94

Question 29

Find the accumulated amount A if the principal P = $13,000 is invested at the interest rate of r = 7% per year for t = 10.5 years, compounded quarterly. Please round your answer to the nearest cent.
A = $__________

Question 30

Find the accumulated amount A if the principal P = $2,000 is invested at the interest rate of r = 5% per year for t = 6 years, compounded annually. Please round your answer to the nearest cent.
A = $ __________

Question 31

Find the effective rate corresponding to nominal rate %/year compounded monthly. Round the answers to the nearest hundredth of percent. ​

A) %
B) %
C) %
D) %
E) %

Question 32

Find the effective rate of interest corresponding to a nominal rate of 6%/year compounded annually, semiannually, quarterly, and monthly. ​

A) The effective rate of interest corresponding to a nominal rate of 6%/year is
6)00% if compounded annually,
6)04% if compounded semi-annually,
6)59% if compounded quarterly,
5)00% if compounded monthly.
​
B) The effective rate of interest corresponding to a nominal rate of 6%/year is
6)00% if compounded annually,
6)59% if compounded semi-annually,
5)00% if compounded quarterly,
6)17% if compounded monthly.
​
C) The effective rate of interest corresponding to a nominal rate of 6%/year is
6)00% if compounded annually,
6)09% if compounded semi-annually,
6)14% if compounded quarterly,
6)17% if compounded monthly.
​

Question 33

Carlos invested $7,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $7,432. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). ​

A) 9.24%.
B) 9.34%.
C) 6.18%.
D) 6.38%.

Question 34

A bank deposit paying simple interest grew from an initial sum of $1,000 to a sum of $1,075 in 9 mo. Find the interest rate.
r = __________ %/year

Question 35

How many days will it take for a sum of $8,000 to earn $240 interest if it is deposited in a bank paying ordinary simple interest at the rate of 5%/year? (Use a 365-day year.)
__________ days

Question 36

If the accumulated amount is $1,640 at the end of 8 years and the simple rate of interest is 8%/year, what is the principal?
P = $ __________

Question 37

Six and a half years ago, Chris invested $9,000 in a retirement fund that grew at the rate of 10.44%/year compounded quarterly. What is his account worth today? Please round the answer to the nearest cent. ​

A) $17,631.72
B) $17,796.97
C) $17,561.76
D) $17,586.30
E) $18,596.31

Question 38

Find the accumulated amount A if the principal P = $170,000 is invested at the interest rate of r = 8% per year for years, compounded monthly. Please round your answer to the nearest cent.
A = $ __________

Question 39

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​
If compound interest is converted annually, then the accumulated amount after t years is not the same as the accumulated amount under simple interest over t years.

A) False. Under compound interest , under simple interest.
For example, if r=7%, P=$1,000, t=1 yr, so under compound interest A=1,070, and under simple interest A=1,070.
B) True. This follows from the definitions of the accumulated amount for compound and simple interest.

Question 40

Georgia purchased a house in 1998 for $190,000. In 2003 she sold the house and made a net profit of $58,000. Find the effective annual rate of return on her investment over the 5-yr period. Please round the answer to the nearest tenth of percent. ​

A) 6.0%/yr
B) 6.6%/yr
C) 5.3%/yr
D) 5.5%/yr
E) 6.9%/yr

Question 41

Find the effective rate corresponding to the given nominal rate 10% compounded semi-annually. Please express your answer as a fraction.

Question 42

Find the effective rate of interest corresponding to a nominal rate of 5%/year compounded annually, semiannually, quarterly, and monthly. Round the answers to two decimal places, if necessary.

Question 43

Georgia purchased a house in 1997 for $220,000. In 2003 she sold the house and made a net profit of $41,000. Find the effective annual rate of return on her investment over the 6-yr period. Please round the answer to the nearest tenth of percent.
__________%/yr

Question 44

A young man is the beneficiary of a trust fund established for him 21 years ago at his birth. If the original amount placed in trust was $5,000, how much will he receive if the money has earned interest at the rate of 6%/year compounded annually? Compounded quarterly? Compounded monthly? Please round your answers to the nearest dollar.
$__________ annually
$__________ quarterly
$__________ monthly

Question 45

Today a typical family of four spends $600/month for food. If inflation occurs at the rate of 4%/year over the next 8 yr, how much should the typical family of four expect to spend for food 8 yr from now? Please round the answer to the nearest cent.
$ __________

Question 46

In the last 3 years, mutual fund A grew at the rate of 10.5%/year compounded quarterly. Over the same period, mutual fund B grew at the rate of 10.6%/year compounded semi-annually. Which mutual fund has a better rate of return? (Answer A or B.)

Question 47

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually. ​

A) $765.77
B) $3,315.38
C) $6,748.10
D) $750.00

Question 48

Find how much money should be deposited in a bank paying interest at the rate of 10.5%/year compounded quarterly so that at the end of 5 years the accumulated amount will be $60,000. Round your answer to the nearest cent.
$ __________

Question 49

Carlos invested $4,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $4,163. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). Round your answer to the nearest hundredth of a percent.
r_eff = __________ %/year

Question 50

Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.
__________ %/yr

Question 51

In order to help finance the purchase of a new house, the Abdullahs have decided to apply for a short-term loan (a bridge loan) in the amount of $180,000 for a term of 2 mo. If the bank charges simple interest at the rate of 13%/year, how much will the Abdullahs owe the bank at the end of the term?
$ __________

Question 52

Find the simple interest on a $500 investment made for 5 years at an interest rate of 9%/year. What is the accumulated amount?

Question 53

The Kwans are planning to buy a house 4 years from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 6%/year during that period. If this economic prediction holds true, how much can the Kwans expect to pay for a house that currently costs $130,000? Please round your answer to the nearest dollar.
$ __________

Question 54

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.87% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? (Enter A or B.)

Question 55

Anthony invested a sum of money 4 yr ago in a savings account that has since paid interest at the rate of 9%/year compounded quarterly. His investment is now worth $22,841.96. How much did he originally invest? Please round the answer to the nearest cent.
$ __________

Question 56

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
​
Susan's salary increased from $55,000/year to $65,000/year over a 6-year period. Therefore, Susan got annual increases of 6% over that period.

Question 57

The future value of an annuity can be found by adding together all the payments that are paid into the account and all the interests they have earned. ​

A) The statement is false.
B) The statement is true.

Question 58

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
​
If compound interest is converted annually, then the accumulated amount after t years is not the same as the accumulated amount under simple interest over t yr.

Question 59

From age 25 to age 40, Jessica deposited $150 at the end of each month into a tax-free retirement account. She made no withdrawals or further contributions until age 65. Alex made deposits of $300 into his tax-free retirement account from age 40 to age 65. If both accounts earned interest at the rate of 5%/year compounded monthly, who ends up with a bigger nest egg upon reaching the age of 65, Jessica or Alex? ​

A) Jessica and Alex will end up with the equal retirement accounts.
B) Jessica will end up with the larger retirement account.
C) Alex will end up with the larger retirement account.

Question 60

Five and a half years ago, Chris invested $9,000 in a retirement fund that grew at the rate of 10.44%/year compounded quarterly. What is his account worth today? Please round the answer to the nearest cent.
$ __________

Question 61

Linda has joined a "Christmas Fund Club" at her bank. At the end of every month, December through October inclusive, she will make a deposit of $30 in her fund. If the money earns interest at the rate of 6%/year compounded monthly, how much will she have in her account on December 1 of the following year? ​

A) $340.07
B) $449.15
C) $30.00
D) $338.37

Question 62

Robin, who is self-employed, contributes $5,500/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 8.5%/year compounded yearly? ​

A) $155,277.48
B) $18,698.59
C) $219,983.36
D) $6,623.25

Question 63

Find the amount of an ordinary annuity for 6 years of quarterly payments of $1,800 that earn interest at 4% per year compounded quarterly. ​

A) $11,073.63
B) $70,348.69
C) $48,552.24
D) $2,285.52

Question 64

Find the amount of an ordinary annuity for 6 years of semiannually payments of $1,400 that earn interest at 8%/year compounded semi-annually. ​

A) $2,241.45
B) $21,036.13
C) $26,567.98
D) $9,286.17

Question 65

Find the present value of the ordinary annuity. Please round the answer to the nearest cent. $5,000 per semiannual period for 5 yr at 11%/year compounded semiannually

A) P = $
B) P = $
C) P = $
D) P = $
E) P = $

Question 66

Find the amount (future value) of the ordinary annuity. Please round the answer to the nearest cent. $200/month for yr at 9%/year compounded monthly.
​

A) S = $
B) S = $
C) S = $
D) S = $
E) S = $

Question 67

If a merchant deposits $2,000 annually at the end of each tax year in an IRA account paying interest at the rate of 4%/year compounded annually, how much will she have in her account at the end of 20 years? Round your answer to two decimal places. ​

A) $4,382.25
B) $59,556.16
C) $3,600.00
D) $25,901.32

Question 68

The Johnsons have accumulated a nest egg of $25,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1,000/month in monthly payments (to take advantage of their tax deductions) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1,800. If local mortgage rates are 9.5%/year compounded monthly for a conventional 40-year mortgage, what is the price range of houses that they should consider? ​
If the Johnsons decide to secure a 20-year mortgage instead of a 40-year mortgage, what is the price range of houses they should consider when the local mortgage rate for this type of loan is 9%?
​

A) The price of houses for 40-yr mortgage lies between $5,461,292 and $9,810,325;
For 20-yr mortgage - between $692,887 and $1,227,196.
B) The price of houses for 40-yr mortgage lies between $148,447 and $247,205;
For 20-yr mortgage - between $136,145 and $225,061.
C) The price of houses for 40-yr mortgage lies between $136,145 and $225,061;
For 20-yr mortgage - between $148,447 and $247,205.

Question 69

Karen has been depositing $150 at the end of each month in a tax-free retirement account since she was 30. Matt, who is the same age as Karen, started depositing $300 at the end of each month in a tax-free retirement account when he was 40. Assuming that both accounts have been and will be earning interest at the rate of 7%/year compounded monthly, who will end up with the larger retirement account at the age of 65, Karen or Matt? ​

A) Matt will end up with the larger retirement account.
B) Karen will end up with the larger retirement account.
C) Karen and Matt will end up with the equal retirement accounts.

Question 70

Pierce Publishing sells encyclopedias under two payment plans: cash or installment. Under the installment plan, the customer pays $23/month over 2 yr with interest charged on the balance at a rate of 15%/year compounded monthly. Find the cash price for a set of encyclopedias if it is equivalent to the price paid by a customer using the installment plan. Please round the answer to the nearest cent. ​

A) $406.93
B) $564.26
C) $420.19
D) $332.81
E) $474.36

Question 71

Find the present value of an ordinary annuity of $150 payments each made monthly over 10 years and earning interest at 4% per year compounded monthly. ​

A) $3,716.11
B) $14,815.53
C) $312.50
D) $1,216.63

Question 72

Luis has $170,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put $4,000/quarter into the new account until his retirement 20 yr from now. If the account earns interest at the rate of 7%/year compounded quarterly, how much will Luis have in his account at the time of his retirement? Please round the answer to the nearest cent. ​
(Hint: Use the compound interest formula and the annuity formula.)
​

A) $1,435,949.35
B) $1,422,687.09
C) $1,226,896.37
D) $1,278,652.02
E) $1,368,261.92

Question 73

Find the present value of an ordinary annuity of $5,000 payments each made annually over 6 years and earning interest at 9% per year compounded annually. ​

A) $7.52
B) $22,429.59
C) $37,616.67
D) $8,385.50

Question 74

Find the amount of an ordinary annuity for years of weekly payments of $ that earn interest at % per year compounded weekly. ​

A) $21,381.98
B) $70.06
C) $350.91
D) $23,182.47

Question 75

Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually. ​

A) $14,148.25
B) $6,954.70
C) $9,763.58
D) $3,365.99

Question 76

Find the present value of an ordinary annuity of $500 payments each made quarterly over 6 years and earning interest at 8% per year compounded quarterly. ​

A) $5,264.38
B) $2,311.44
C) $9,456.96
D) $24,968.07

Question 77

Lupe made a down payment of $1,500 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 12%/year compounded monthly. Under the terms of her finance agreement, she is required to make payments of $250/month for 30 month. What is the cash price of the car? ​

A) $10,196.22
B) $6,451.93
C) $3,513.80
D) $7,951.93

Question 78

A state lottery commission pays the winner of the "Million Dollar" lottery 20 installments of $50,000/year. The commission makes the first payment of $50,000 immediately and the other payments at the end of each of the next 19 yr. Determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of 9%/year compounded yearly. Please round the answer to the nearest cent. ​
(Hint: Find the present value of an annuity.)
​

A) $356,042.19
B) $497,505.74
C) $551,774.91
D) $587,083.64
E) $430,139.31

Question 79

The Betzes have leased an auto for 2 year at $600/month. If money is worth 8%/year compounded monthly, what is the equivalent cash payment (present value) of this annuity? ​

A) $6,317.25
B) $13,266.33
C) $1,069.96
D) $15,559.91

Question 80

As a fringe benefit for the past 8 years, Colin's employer has contributed $50 at the end of each month into an employee retirement account for Colin that pays interest at the rate of 8%/year compounded monthly. Colin has also contributed $2,000 at the end of each of the last 4 years into an IRA that pays interest at the rate of 10%/year compounded yearly. How much does Colin have in his retirement fund at this time? ​

A) $9,282.00
B) $9,813.83
C) $6,693.43
D) $15,975.43