Question 1

Payday loans are very short-term loans that charge very high interest rates.You can borrow $600 today and repay $675 in two weeks.What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?
A) 12.89 percent
B) 13.28 percent
C) 2037.71 percent
D) 113.28 percent

Accepted Answer

((1 + 0.125)^26) − 1 = 2037.71 percent.

Question 2

Payday loans are very short-term loans that charge very high interest rates.You can borrow $500 today and repay $550 in two weeks.What is the compound annual rate implied by this 10 percent rate charged for only two weeks?
A) 10.50 percent
B) 12.00 percent
C) 1091.78 percent
D) 110.50 percent

Accepted Answer

(1 + 0.10)^26 − 1 = 1091.78 percent.

Question 3

Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt.If she can pay $200 each month and the card charges 17 percent APR (compounded monthly),how long will it take her to pay off the debt?
A) 28.63 months
B) 35.00 months
C) 47.71 months
D) 48.68 months

Accepted Answer

PV = 7000, I = 17/12 = 1.416667, FV = 0, PMT = −200, CPT N = 48.68

Question 4

What is the interest rate of a 6-year,annual $3,000 annuity with present value of $14,000?
A) 5.64 percent
B) 7.69 percent
C) 10.17 percent
D) 11.32 percent

Accepted Answer

N = 6, PV = − 14000, PMT = 3000, FV = 0, CPT I = 7.69

Question 5

Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt.If he can pay $200 each month and the card charges 20 percent APR (compounded monthly),how long will it take him to pay off the debt?
A) 17.40 months
B) 20.00 months
C) 24.04 months
D) 24.53 months

Accepted Answer

PV = 4000, I = 20/12 = 1.6667, FV = 0, PMT = −200, CPT N = 24.53

Question 6

Phoebe realizes that she has charged too much on her credit card and has racked up $10,000 in debt.If she can pay $300 each month and the card charges 18 percent APR (compounded monthly),how long will it take her to pay off the debt?
A) 27.23 months
B) 33.33 months
C) 46.56 months
D) 69.70 months

Accepted Answer

PV = 10000, I = 18/12 = 1.5, FV = 0, PMT = −300, CPT N = 46.56

Question 7

What is the interest rate of a 4-year,annual $1,000 annuity with present value of $3,500?
A) 3.85 percent
B) 5.56 percent
C) 8.84 percent
D) 9.70 percent

Accepted Answer

N = 4, PV = −3500, PMT = 1000, FV = 0, CPT I = 5.56

Question 8

You wish to buy a $20,000 car.The dealer offers you a 5-year loan with an 8 percent APR.What are the monthly payments?
A) $272.19
B) $333.33
C) $405.53
D) $4,080.35

Accepted Answer

N = 5 × 12 = 60, PV = 20000, I = 8/12 = 0.6667, FV = 0, CPT PMT = −405.53

Question 9

What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?
A) 2.37 percent
B) 5.77 percent
C) 6.00 percent
D) 13.53 percent

Accepted Answer

N = 4 × 12 = 48, PV = 0, PMT = −500, FV = 27050, CPT I = 6.00

Question 10

Payday loans are very short-term loans that charge very high interest rates.You can borrow $200 today and repay $250 in two weeks.What is the compound annual rate implied by this 25 percent rate charged for only two weeks?
A) 26.60 percent
B) 32,987.22 percent
C) 30.00 percent
D) 128.25 percent

Accepted Answer

((1 + 0.25)^26) − 1 = 32,987.22 percent.

Question 11

Given a 6 percent interest rate,compute the present value of deposits made in years 1,2,3,and 4 of $1,200,$1,400,$1,400,and $1,500.
A) $4,356.52
B) $4,741.68
C) $5,188.68
D) $5,506.00

Accepted Answer

The answer of Given a 6 percent interest rate,compute the...

Question 12

A small business owner visits his bank to ask for a loan.The owner states that he can repay a loan at $2,000 per month for the next three years and then $1,000 per month for the two years after that.If the bank is charging customers 8.5 percent APR,how much would it be willing to lend the business owner?
A) $80,419.29
B) $6,494.66
C) $21,780.74
D) $96,000.00

Accepted Answer

N = 5 × 12 = 60, I = 8.5/12 = 0.7083, FV = 0, PMT = 1000, CPT PV = 48741.18
N = 2 × 12 = 24, I = 8.5/12 = 0.7083, FV = 0, PMT = 1000 (2000 − 1000), CPT PV = 31678.11
sum of PV = 80419.29.

Question 13

If you start making $25 monthly contributions today and continue them for four years,what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?
A) $101.26, $99.26
B) $1,352.45, $1,064.51
C) $1,359.21, $1,069.83
D) $2,171.02, $1,516.03

Accepted Answer

N = 4 × 12 = 48, I = 6/12 = 0.5, PV = 0, PMT = 25, CPT FV = 1359.21
N = 4 × 12 = 48, I = 6/12 = 0.5, FV = 0, PMT = 25, CPT PV = 1069.83

Question 14

Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt.If he can pay $150 each month and the card charges 18 percent APR (compounded monthly),how long will it take him to pay off the debt?
A) 13.03 months
B) 14.68 months
C) 20.00 months
D) 23.96 months

Accepted Answer

PV = 3000, I = 18/12 = 1.5, FV = 0, PMT = −150, CPT N = 23.96

Question 15

A small business owner visits his bank to ask for a loan.The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for the two years after that.If the bank is charging customers 5.5 percent APR,how much would it be willing to lend the business owner?
A) $4,046.90
B) $59,293.50
C) $24,261.00
D) $66,000.00

Accepted Answer

N = 5 × 12 = 60, I = 5.5/12 = 0.4583, FV = 0, PMT = 500, CPT PV = 26176.42
N = 3 × 12 = 36, I = 5.5/12 = 0.4583, FV = 0, PMT = 1000 (1500 − 500), CPT PV = 33117.08
sum of PV = 59293.50.

Question 16

You wish to buy a $15,000 car.The dealer offers you a 4-year loan with a 9 percent APR.What are the monthly payments?
A) $260.78
B) $312.50
C) $373.28
D) $3,820.56

Accepted Answer

N = 4 × 12 = 48, PV = 15000, I = 9/12 = 0.75, FV = 0, CPT PMT = −373.28

Question 17

A perpetuity pays $100 per year and interest rates are 6.5 percent.How much would its value change if interest rates increased to 9 percent?
A) $250.00 increase
B) $250.00 decrease
C) $427.35 increase
D) $427.35 decrease

Accepted Answer

$100/0.065 = $1538.46, $100/0.09 = $1111.11.
change = 1538.46 − 1111.11 = 427.35 decrease.

Question 18

If you start making $100 monthly contributions today and continue them for five years,what is their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?
A) $508.14, $487.74
B) $512.64, $491.80
C) $7,743.71, $4,706.53
D) $7,808.24, $4,745.78

Accepted Answer

N = 5 × 12 = 60, I = 10/12 = 0.83, PV = 0, PMT = 100, CPT FV = 7808.24
N = 5 × 12 = 60, I = 10/12 = 0.83, FV = 0, PMT = 100, CPT PV = 4745.78

Question 19

A perpetuity pays $50 per year and interest rates are 9 percent.How much would its value change if interest rates decreased to 6 percent?
A) $150.00 increase
B) $150.00 decrease
C) $277.78 increase
D) $277.78 decrease

Accepted Answer

$50/0.09 = $555.55, $50/0.06 = $833.33.
change = 555.55 − 833.33 = 277.78 increase.

Question 20

What annual interest rate would you need to earn if you wanted a $200 per month contribution to grow to $14,700 in five years?
A) 6.47 percent
B) 7.76 percent
C) 8.01 percent
D) 14.70 percent

Accepted Answer

N = 5 × 12 = 60, PV = 0, PMT = −200, FV = 14700, CPT I = 8.00

Quiz 5: Time Value of Money 2: Analyzing Annuity Cash Flows

Payday loans are very short-term loans that charge very high interest rates.You can borrow $600 today and repay $675 in two weeks.What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?

Payday loans are very short-term loans that charge very high interest rates.You can borrow $500 today and repay $550 in two weeks.What is the compound annual rate implied by this 10 percent rate charged for only two weeks?

Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt.If she can pay $200 each month and the card charges 17 percent APR (compounded monthly) ,how long will it take her to pay off the debt?

What is the interest rate of a 6-year,annual $3,000 annuity with present value of $14,000?

Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt.If he can pay $200 each month and the card charges 20 percent APR (compounded monthly) ,how long will it take him to pay off the debt?

Phoebe realizes that she has charged too much on her credit card and has racked up $10,000 in debt.If she can pay $300 each month and the card charges 18 percent APR (compounded monthly) ,how long will it take her to pay off the debt?

What is the interest rate of a 4-year,annual $1,000 annuity with present value of $3,500?

You wish to buy a $20,000 car.The dealer offers you a 5-year loan with an 8 percent APR.What are the monthly payments?

What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?

Payday loans are very short-term loans that charge very high interest rates.You can borrow $200 today and repay $250 in two weeks.What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

Given a 6 percent interest rate,compute the present value of deposits made in years 1,2,3,and 4 of $1,200,$1,400,$1,400,and $1,500.

If you start making $25 monthly contributions today and continue them for four years,what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?

Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt.If he can pay $150 each month and the card charges 18 percent APR (compounded monthly) ,how long will it take him to pay off the debt?

You wish to buy a $15,000 car.The dealer offers you a 4-year loan with a 9 percent APR.What are the monthly payments?

A perpetuity pays $100 per year and interest rates are 6.5 percent.How much would its value change if interest rates increased to 9 percent?

If you start making $100 monthly contributions today and continue them for five years,what is their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?

A perpetuity pays $50 per year and interest rates are 9 percent.How much would its value change if interest rates decreased to 6 percent?

What annual interest rate would you need to earn if you wanted a $200 per month contribution to grow to $14,700 in five years?