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

Question 1

When computing the future value of an annuity, the higher the compound frequency

A) the lower the future value will be.
B) the higher the future value will be.
C) the less likely the future value can be calculated.
D) the more likely the future value can be calculated.

Answer 1

the higher the future value will be.

Question 2

The simple form of an annualized interest rate is called the annual percentage rate (APR). The effective annual rate (EAR) is a

A) less accurate measure of the interest rate paid for monthly compounding.
B) more accurate measure of the interest rate paid for monthly compounding.
C) concept that is only used because the law requires it, and is of no use to a borrower.
D) measure that only applies to mortgages.

Answer 2

more accurate measure of the interest rate paid for monthly compounding.

Question 3

When you get your credit card bill, it will offer a minimum payment, which

A) usually only pays the accrued interest and a small amount of principal.
B) usually only pays the principal and a small amount of accrued interest.
C) usually only pays the principal and no accrued interest.
D) usually only pays the accrued interest and no principal.

Answer 3

usually only pays the accrued interest and a small amount of principal.

Question 4

An annuity due:

A) is an annuity in which the cash flows occur at the beginning of each period.
B) makes the cash flow in the beginning of year 1 look like it's a cash flow of today.
C) moves the cash flow from the end of the year to the beginning, which looks like the end of the previous year.
D) the appropriate tax rate.

Question 5

Which of the following statements about annual percentage rate (APR) and effective annual rate (EAR) are not true?

A) The annual percentage rate (APR) is considered a more accurate measurement of what you will actually pay.
B) Lenders are legally required to show potential borrowers the effective annual rate (EAR) on any loan offered.
C) The difference between APR and EAR is not that large.
D) None of the above are untrue statements.

Question 6

To compute the present or future value of an annuity due, one computes the value of an ordinary annuity and then

A) multiplies it by (1 + i).
B) divides it by (1 + i).
C) multiplies it by (1 − i).
D) divides it by (1 − i).

Question 7

Compounding monthly versus annually causes the interest rate to be effectively higher, and thus the future value

A) grows.
B) decreases.
C) is independent of the monthly compounding.
D) is affected only if the calculation involves an annuity due.

Question 8

Your credit rating and current economic conditions will determine

A) whether you get simple or compound interest.
B) how long compounding will affect you.
C) how long discounting will affect you.
D) the interest rate that a lender will offer.

Question 9

Level sets of frequent, consistent cash flows are called

A) loans.
B) budgets.
C) annuities.
D) bills.

Question 10

Loan amortization schedules show

A) the principal balance paid per period only.
B) the interest paid per period only.
C) both the principal balance and interest paid per period.
D) the present value of the payments due.

Question 11

When interest rates are lower, borrowers can

A) get loans more easily.
B) cannot get loans as easily.
C) borrow more money.
D) afford higher payments.

Question 12

In order to discount multiple cash flows to the present, one would use

A) the appropriate compound rate.
B) the appropriate discount rate.
C) the appropriate simple rate.
D) the appropriate tax rate.

Question 13

When moving from the left to the right of a time line, we are using

A) compound interest to calculate future values.
B) discounted cash flows to calculate present values.
C) only payments to calculate future values.
D) simple interest to calculate future values.

Question 14

A perpetuity, a special form of annuity, pays cash flows

A) and is not effected by interest rate changes.
B) that do not have time value of money implications.
C) continuously for one year.
D) periodically forever.

Question 15

The present value of annuity payments made far into the future is

A) worth very little today.
B) worth much more today.
C) valued as having no time value of money.
D) valued as worthless as their value is not determinable.

Question 16

When saving for future expenditures, we can add the ________ of contributions over time to see what the total will be worth at some point in time.

A) present value
B) future value
C) time value to money
D) payment

Question 17

Many people who want to start investing for their future want to start today, which implies an annuity stream that is paid at the beginning of the period. Beginning-of-period cash flows are referred to as

A) ordinary annuities.
B) annuities due.
C) perpetuities.
D) present values.

Question 18

People refinance their home mortgages

A) when rates fall.
B) when rates rise.
C) when rates fall and rise.
D) whenever they need to, independent of rates.

Question 19

Which of the following statements about compound frequency is not true?

A) Compounding frequency can only be annual, semi-annual or quarterly.
B) The higher the compound frequency, the higher the future value will be.
C) The relative increase in value from increasing compounding frequency seems to diminish with increasing frequencies.
D) None of the above are untrue statements.

Question 20

The length of time of the annuity is very important in accumulating wealth within an annuity. What other factor also has this effect?

A) the time line
B) interest rate for compounding
C) the present value
D) the future value

Question 21

What is the present value of a $500 deposit in year 1, and another $100 deposit at the end of year 4 if interest rates are 5 percent?

A) $480.00
B) $493.62
C) $558.46
D) $582.27

Question 22

What is the present value of a $300 annuity payment over 5 years if interest rates are 8 percent?

A) $204.17
B) $440.80
C) $1,197.81
D) $1,938.96

Question 23

If the future value of an ordinary, 7-year annuity is $10,000 and interest rates are 4 percent, what is the future value of the same annuity due?

A) $9,615.38
B) $10,000.00
C) $10,400.00
D) $10,700.00

Question 24

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

A) $4,741.68
B) $5,986.26
C) $6,179.80
D) $6,726.16

Question 25

What is the future value of an $800 annuity payment over 15 years if the interest rates are 6 percent?

A) $1,917.25
B) $7,002.99
C) $12,720.00
D) $18,620.78

Question 26

Compute the future value in year 10 of a $1,000 deposit in year 1, and another $1,500 deposit at the end of year 4 using an 8 percent interest rate.

A) $3,120.73
B) $4,379.31
C) $4,500.00
D) $5,397.31

Question 27

What is the present value of a $600 annuity payment over 4 years if interest rates are 6 percent?

A) $475.26
B) $757.49
C) $2,079.06
D) $3,145.28

Question 28

Assume that you contribute $200 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $400 per month for another 25 years. Given a 5 percent interest rate, what is the value of your retirement plan after 40 years?

A) $424,305.97
B) $24,159.95
C) $28,475.66
D) $72,479.86

Question 29

What is the present value of a $250 deposit in year 1, and another $50 deposit at the end of year 6 if interest rates are 10 percent?

A) $120.00
B) $169.34
C) $255.50
D) $278.22

Question 30

A loan is offered with monthly payments and a 6.5 percent APR. What is the loan's effective annual rate (EAR)?

A) 5.69 percent
B) 6.697 percent
C) 7.28 percent
D) 12.63 percent

Question 31

If the future value of an ordinary, 4-year annuity is $1,000 and interest rates are 6 percent, what is the future value of the same annuity due?

A) $943.40
B) $1,000.00
C) $1,040.00
D) $1,060.00

Question 32

A loan is offered with monthly payments and a 10 percent APR. What is the loan's effective annual rate (EAR)?

A) 10.00 percent
B) 10.47 percent
C) 11.20 percent
D) 12.67 percent

Question 33

If the present value of an ordinary, 4-year annuity is $1,000 and interest rates are 6 percent, what is the present value of the same annuity due?

A) $943.40
B) $1,000.00
C) $1,040.00
D) $1,060.00

Question 34

What is the future value of a $1,000 annuity payment over 4 years if the interest rates are 8 percent?

A) $3,312.10
B) $4,320.00
C) $4,506.11
D) $9,214.20

Question 35

Given a 4 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.

A) $4,334.53
B) $5,070.78
C) $5,191.68
D) $5,484.56

Question 36

What is the present value, when interest rates are 6.5 percent, of a $100 payment made every year forever?

A) $6.50
B) $650.00
C) $1,000.00
D) $1,538.46

Question 37

Compute the future value in year 4 of a $500 deposit in year 1, and another $1,000 deposit at the end of year 3 using a 5 percent interest rate.

A) $1,625.00
B) $1,628.81
C) $1,800.00
D) $1,823.26

Question 38

What is the present value, when interest rates are 10 percent, of a $75 payment made every year forever?

A) $6.75
B) $675.00
C) $750.00
D) $1,000.00

Question 39

Assume that you contribute $100 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $200 per month for another 20 years. Given a 6 percent interest rate, what is the value of your retirement plan after 40 years?

A) $225,353
B) $19,155
C) $245,353
D) $199,359

Question 40

When you get your credit card bill, if you make a payment larger than the minimum payment

A) you are wasting your current consumption and making TVM not work for you.
B) you will reduce the payoff time.
C) you will increase the payoff time.
D) you will not affect the payoff time.

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

Given a 7 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,500, and $1,500.

A) $3,967.06
B) $4,351.50
C) $4,859.81
D) $5,207.00

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

Given a 4 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.

A) $4,103.06
B) $4,334.53
C) $4,615.38
D) $4,804.00

Question 55

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) 2037.79 percent
D) 113.28 percent

Question 56

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

Question 57

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, $4,745.76

Question 58

Given a 5 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,400, $1,400, and $1,500.

A) $4,360.32
B) $4,665.65
C) $5,047.62
D) $5,305.00

Question 59

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) 1091.82 percent
D) 110.50 percent

Question 60

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

Question 61

What is the present value of a $775 annuity payment over six years if interest rates are 11 percent?

A) $3,017.84
B) $3,119.67
C) $3,202.92
D) $3,278.67

Question 62

If the future value of an ordinary, 11-year annuity is $5,575 and interest rates are 5.5 percent, what is the future value of the same annuity due?

A) $5,619.52
B) $5,769.06
C) $5,881.63
D) $5,947.88

Question 63

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

Question 64

Ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $2,500 monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal?

A) $895.95
B) $902.47
C) $1,947.88
D) $2,500.00

Question 65

Monica has decided that she wants to build enough retirement wealth that, if invested at 7 percent per year, will provide her with $3,000 monthly income for 30 years. To date, she has saved nothing, but she still has 20 years until she retires. How much money does she need to contribute per month to reach her goal?

A) $671.78
B) $865.62
C) $3,000.00
D) $7,025.77

Question 66

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

Question 67

Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,500 and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $2,000 is made in year 5.

A) $1,909.42
B) $3,272.41
C) $3,433.60
D) $5,656.34

Question 68

A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

A) 4.89 percent, 7.72 percent respectively
B) 5.00 percent, 8.00 percent respectively
C) 5.12 percent, 8.30 percent respectively
D) 12.59 percent, 12.65 percent respectively

Question 69

A car company is offering a choice of deals. You can receive $2,000 cash back on the purchase, or a 2 percent APR, 3-year loan. The price of the car is $17,000 and you could obtain a 3-year loan from your credit union, at 7 percent APR. Which deal is cheaper?

A) the car company's 2 percent 3-year loan
B) the rebate with the credit union's 7 percent 3-year loan

Question 70

Given a 7 percent interest rate, compute the year 6 future value if deposits of $2,500 and $1,500 are made in years 2 and 3, respectively, and a withdrawal of $900 is made in year 4.

A) $2,721.44
B) $4,084.15
C) $4,491.60
D) $7,059.04

Question 71

If the present value of an ordinary, 8-year annuity is $12,500 and interest rates are 9.1 percent, what is the present value of the same annuity due?

A) $13,637.50
B) $13,941.90
C) $14,114.80
D) $14,211.90

Question 72

A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5.5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8.5 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

A) 5.37 percent, 8.19 percent respectively
B) 5.50 percent, 8.50 percent respectively
C) 5.64 percent, 8.84 percent respectively
D) 12.60 percent, 12.66 percent respectively

Question 73

Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10 percent interest rate.

A) $12,510.77
B) $12,909.81
C) $13,406.73
D) $15,007.52

Question 74

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

Question 75

Bill makes $100 payments at the end of each year for 5 years. If interest rates are 8%, what is the present value of this annuity stream?

A) $500
B) $399.27
C) $475
D) $455.63

Question 76

Compute the present value of a $2,500 deposit in year 4 and another $10,000 deposit at the end of year 8 if interest rates are 15 percent.

A) $4,211.26
B) $4,572.19
C) $4,698.40
D) $4,901.57

Question 77

What is the future value of a $500 annuity payment over eight years if interest rates are 14 percent?

A) $6,241.09
B) $6,616.38
C) $6,750.14
D) $6,809.72

Question 78

Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What is the minimum price Hank would need to receive for his car?

A) $8,000.00
B) $12,079.65
C) $12,941.12
D) $15,133.64

Question 79

What is the present value of a $1,100 payment made every year forever when interest rates are 4.5 percent?

A) $11,100
B) $21,089.37
C) $22,963.14
D) $24,444.44

Question 80

If you are saving for a plane ticket for a future vacation and you deposit $200 today, followed by $250 at the end of the first year, and a $300 deposit at the end of the second year, what will the future value of your deposits be in 3 years if the interest rates are 5%?

A) $750
B) $822.15
C) $787.5
D) None of the above