Deck 4: Present Value

Question 1

If the present value of $3,000 to be received after a year is $2,795, the annual rate of discount must be

A)5.65%.
B)7.33%.
C)9%.
D)11.11%.

Answer 1

B

Question 2

In the one-period present-value equation, P = F/(1 + i), the term 1 + i is referred to as

A)future value.
B)present value.
C)the rate of discount.
D)the discount factor.

Answer 2

D

Question 3

The equation that allows us to compare dollar amounts to be received at different dates is the

A)present-value formula.
B)Taylor rule.
C)interest-rate parity equation.
D)​Roy's identity

Answer 3

A

Question 4

If the principal invested in a bank at an annual interest rate of 6% is $3,000, the interest that will accumulate on the principal after a year will equal

A)$180.
B)$300.
C)$500.
D)$700.

Question 5

Discounting is the process of dividing a future value by the_____ to obtain the_____ value.

A)discount factor; past
B)discount factor; present
C)rate of discount; past
D)rate of discount; present

Question 6

Consider a bond that has a present value of $1,000.If the annual rate of interest is 7 percent, the future value of the bond after a year is

A)$930.00.
B)$934.58.
C)$1,000.00.
D)$1,070.00.

Question 7

Earning interest on the interest that was earned in prior years is referred to as

A)discounting.
B)compounding.
C)present valuing.
D)bonding.

Question 8

A debt security with just one payment at a future date is referred to as a

A)coupon bond.
B)fixed-payment security.
C)discount bond.
D)perpetuity.

Question 9

Consider a bond that has a present value of $1,500.If the annual rate of interest is 4 percent, the future value of the bond after a year is

A)$1,560.00.
B)$1,540.00.
C)$1,440.00.
D)$1,442.31.

Question 10

Consider a one-year discount bond that pays $1,000 at maturity.If the annual rate of discount is 7 percent, the present value of the bond is

A)$930.00.
B)$934.58.
C)$993.00.
D)$993.46.

Question 11

The amount of money that you would need to invest today to yield a given future amount is called the

A)future value.
B)present value.
C)rate of discount.
D)discount factor.

Question 12

The present value of a security is

A)directly related to the discount rate.
B)inversely related to the time until maturity.
C)directly related to the principal amount.
D)is not related to the discount rate.

Question 13

In the one-period present-value equation, P = F/(1 + i), the term i is known as

A)future value.
B)present value.
C)the rate of discount.
D)the discount factor.

Question 14

The present value of a series of future payments is

A)inversely related to the future value.
B)unrelated to the discount factor.
C)inversely related to the rate of discount.
D)directly related to the discount factor.

Question 15

Which of the following options would you choose to have if the rate of discount is 20 percent?

A)$300 in one year
B)$350 in two years
C)$420 in three years
D)$1500 in ten years

Question 16

Which of the following statements is true?

A)Everything else remaining unchanged, higher the future value of an investment, higher will be the present value.
B)Everything else remaining unchanged, higher the rate of discount on an investment, higher will be the present value.
C)​The future value of an investment is unrelated to the principal amount invested.
D)​​The future value of an investment is unrelated to the ongoing rate of interest.

Question 17

​Treasury bills issued by the U.S.government that mature in a year or less are similar to

A)​perpetuities.
B)​discount bonds.
C)​coupon bonds.
D)​fixed­income securities.

Question 18

​If the interest accumulated on a principal amount of $5,000 at the end of a year is $400, the annual rate of interest must be

A)​4%.
B)​6%.
C)​8%.
D)20%.

Question 19

The amount of money invested in a financial security or deposited into a financial intermediary is referred to as the

A)principal.
B)interest.
C)yield.
D)capital-gain.

Question 20

Consider a one-year discount bond that pays $1,500 one year from now.If the annual rate of discount is 4 percent, the present value of the bond is

A)$1,560.00.
B)$1,540.00.
C)$1,440.00.
D)$1,442.31.

Question 21

Consider a coupon bond that pays $105 every year and repays its principal amount of $1,500 at the end of 3 years.If the annual rate of discount is 7 percent, the present value of the bond is approximately

A)$735.35.
B)$765.00.
C)$1,395.00.
D)$1,500.00.

Question 22

​Which of the following statements is true of a perpetuity?

A)​A perpetuity has a fixed maturity.
B)​The present value of each payment made by a perpetuity is less than the previous payment.
C)​The present value of a perpetuity that pays $100 every year when the annual rate of discount is 5% is $1,000.
D)​​The present value of a perpetuity that pays $200 every year when the annual rate of discount is 7% is $1,750.

Question 23

Consider a three-year fixed-payment security that has a present value of $1,000.If the annual rate of discount is 7 percent, the payment made at the end of each year is

A)$70.00.
B)$107.00.
C)$142.86.
D)$381.05.

Question 24

The difference between the present value of a perpetuity that pays $250 every year and a perpetuity that pays $500 every year when the annual rate of discount is 5% is

A)$500.
B)$750.
C)$5,000.
D)$7,500.

Question 25

Consider a five-year fixed-payment security that has a present value of $1,500.If the annual rate of discount is 2 percent, the payment made at the end of each year is

A)$231.77.
B)$288.24.
C)$300.00.
D)$310.00.

Question 26

A debt security that pays interest forever and never repays the principal is a

A)fiduciary obligation.
B)federal funds loans.
C)perpetuity.
D)junk bond.

Question 27

After amortizing the principal, a debt security that makes the same dollar payment every year is referred to as a

A)coupon bond.
B)fixed-payment security.
C)discount bond.
D)perpetuity.

Question 28

Which of the following statements is true?

A)A coupon bond is a debt security with only one payment.
B)The amount invested in a financial security is referred to as perpetuity.
C)A coupon bond is a debt security that pays interest forever and never repays principal.
D)The present value of a perpetuity varies directly with the annual repayments.

Question 29

The process in which the principal amount of a security is repaid gradually over time is referred to as

A)securitization.
B)depreciation.
C)amortization.
D)discounting.

Question 30

Consider a perpetuity that pays $100 every year.If the annual rate of discount is 7 percent, the present value of the perpetuity is

A)$107.00.
B)$1,300.00.
C)$1,428.57.
D)$1,700.00.

Question 31

The present value of a perpetuity that pays $F every year when the annual rate of discount is i is

A)F/(1 + i).
B)F×i.
C)F/i.
D)F + i.

Question 32

Consider a coupon bond that pays $100 every year and repays its principal amount of $1,000 at the end of 10 years. If the annual rate of discount is 10 percent, the present value of the bond is approximately

A)$909.09.
B)$990.00.
C)$1,000.00.
D)$1,100.00.

Question 33

​Consider a fixed­payment security that pays $100 at the end of every year for five years.If the annual rate of discount is 7 percent, the present value of the security is

A)​$142.64.
B)​$410.02.
C)​$789.34.
D)​$999.63.

Question 34

Consider a perpetuity making one payment each year that has a present value of $1,500.If the annual rate of discount is 3 percent, the annual payment is

A)$15.00.
B)$45.00.
C)$500.00.
D)$1,500.00.

Question 35

Consider a fixed-payment security that pays $100 at the end of every year for three years.If the annual rate of discount is 10 percent, the present value of the security is

A)$24.87.
B)$248.69.
C)$294.10.
D)$1,000.00.

Question 36

Consider a perpetuity that pays $150 every year.If the annual rate of discount is 4 percent, the present value of the perpetuity is

A)$210.00.
B)$3,000.00.
C)$3,600.00.
D)$3,750.00.

Question 37

The amount repaid by a coupon bond at maturity is called its_____ value.

A)present
B)future
C)face
D)coupon

Question 38

Consider a three-year coupon bond that has a present value of $2,000.If the annual rate of discount is 7 percent, and the payment made at the end of each year is $140, the principal amount to be repaid at the end of three years is

A)$1,860.00.
B)$2,000.00.
C)$2,140.00.
D)$2,156.40.

Question 39

Consider a perpetuity making one payment each year that has a present value of $1,000.If the annual rate of discount is 7 percent, the annual payment is

A)$70.00.
B)$107.00.
C)$1,428.57.
D)$14,285.71.

Question 40

A bond that makes a regular interest payment until maturity, at which time the face value is repaid is referred to as a

A)coupon bond.
B)fixed-payment security.
C)discount bond.
D)perpetuity.

Question 41

Suppose you take out a home equity loan of $100,000 for 5 years at an annual interest rate of 5 percent, with payments to be made monthly.What will the approximate monthly payments be? The relevant formula is: $$F = P \times \frac { i } { 1 - \left( \frac { 1 } { 1 + i } \right) ^ { N } }$$ .

A)$1,320.71
B)$1,887.12
C)$1,924.79
D)$5,282.82

Question 42

According to the Truth-in-Savings Act, the interest rate that banks are required to report when you deposit money in an account is known as

A)capital-gains yield.
B)annual percentage yield.
C)current yield.
D)total return.

Question 43

Consider a one-year discount bond that has a present value of $3,000.If the annual rate of discount is 5 percent, calculate the future value of the bond (the amount the bond pays in one year).

Question 44

Consider a one-year discount bond that pays $2,000 one year from now.If the annual rate of discount is 3 percent, calculate the present value of the bond.

Question 45

Past return refers to the

A)highest annual return that a security has produced in the past.
B)mode of the annual returns that a security has produced in the past.
C)average of the annual returns that a security has produced in the past.
D)median of the annual returns that a security has produced in the past.

Question 46

Consider a coupon bond that pays $150 every year and repays its principal amount of $1,500 at the end of five years. If the annual rate of discount is 7 percent, the present value of the bond is approximately

A)$214.29.
B)$808.39.
C)$1,684.50.
D)$1,742.52.

Question 47

Consider a coupon bond that pays $100 every year and repays its principal amount of $1,000 at the end of four years.If the annual rate of discount is 8 percent, the present value of the bond is

A)$671.01.
B)$1,066.24
C)$1,134.20.
D)$1,250.00.

Question 48

According to the theory underlying the present-value formula, would a rational individual prefer to receive (a) $75 one year from now, (b) $85 two years from now, or (c) $90 three years from now, or would he be indifferent between all three choices? Assume that the relevant annual market interest rate is 10 percent and will remain at 10 percent for the next three years?

A)He will prefer $75 one year from now.
B)He will prefer $85 two years from now.
C)He will prefer $90 three years from now.
D)He will be indifferent between all three choices.

Question 49

Consider a two-year coupon bond that has a present value of $10,000.If the rate of discount is 3 percent, and the payment made at the end of each year is $300, the principal amount to be repaid at the end of two years is

A)$10,000.00.
B)$10,300.00.
C)$33,333.33.
D)$333,333.33.

Question 50

John spends $4,000 on a perpetuity that pays $150 each year.The yield to maturity of this perpetuity is

A)1.5%.
B)3.75%.
C)6.2 %.
D)15%.

Question 51

If the annual rate of interest in a market is 12%, the monthly rate of discount will equal

A)1%.
B)12%.
C)24%.
D)144%.

Question 52

Consider a one-year coupon bond that has a present value of $2,000.If the annual rate of discount is 5 percent, and the payment made at the end of each year is $140, the principal amount to be repaid at the end of one year is

A)$1,234.65.
B)$1,363.32.
C)$1,960.00.
D)$2,000.00.

Question 53

​Consider the returns on four investment options: A, B, C, and D.All four investment options require the same principal amount, and the returns on the investments are considered over the same time frame.The present value of the return on investment A is greater than the present value of the return on investment B, which is greater than the present value of the return on investment C.The present value of the return on investment D is the lowest.A rational investor will choose to invest in:

A)option A.
B)option B.
C)​option C.
D)​option D.

Question 54

Your favorite magazine, Fun with Present Value, offers you four different subscription deals for the next four years.It has guaranteed its current and future subscription rates, as shown below.Which will you take, if your annual rate of discount is 6 percent and you want to get the magazine for four years?

A)A one-year subscription for $24, followed by a one-year renewal each year for $24 each year.
B)A two-year subscription for $45, followed by a two-year renewal for $48.
C)A three-year subscription for $72, followed by a one-year renewal for $24.
D)A four-year subscription for $89.

Question 55

Consider a perpetuity that pays $300 every year.If the rate of discount is 6 percent, calculate the present value of the bond.

Question 56

Consider a two-year coupon bond that has a present value of $10,000.If the annual rate of discount is 3 percent, and the payment made at the end of each year is $250, the principal amount to be repaid at the end of two years is

A)$10,101.50.
B)$10,300.00.
C)$13,333.33.
D)$13,583.33.

Question 57

A rise in the annual interest rates will cause

A)​the principal amount of a bond to increase.
B)​​the principal amount of a bond to decrease.
C)​the present value of a bond to decrease.
D)​the present value of a bond to increase.

Question 58

You are considering buying a discount bond that costs $1,000 today and pays you $1,200 in one year.However, there is a 10 percent chance that the company issuing the bond will go bankrupt and not pay you your interest or return your principal.What is the expected return on the bond?

A)20 percent.
B)10 percent.
C)8 percent.
D)−4 percent.

Question 59

According to the theory underlying the present-value formula, would a rational individual prefer to receive (a) $75 one year from now, (b) $85 two years from now, or (c) $90 three years from now, or would he be indifferent between all three choices? Assume that the relevant annual market interest rate is 20 percent and will remain at 20 percent for the next three years?

A)He will prefer $75 one year from now.
B)He will prefer $85 two years from now.
C)He will prefer $90 three years from now.
D)He will be indifferent between all three choices.

Question 60

Suppose you take out a car loan of $10,000 for 3 years at an annual interest rate of 8 percent, with payments to be made monthly.What will be the approximate monthly payments? The relevant formula is: $$F = P \times \frac { i } { 1 - \left( \frac { 1 } { 1 + i } \right) ^ { N } }$$ .

A)$313.36.
B)$323.36.
C)$853.45.
D)$3,880.34.

Question 61

Consider a coupon bond that pays $350 every year and repays its principal amount of $5,000 at the end of four years.If the annual rate of discount is 6 percent, what is the present value of the bond?

Question 62

Consider a fixed-payment security that pays $250 at the end of every year for eight years.If the annual rate of discount is 3 percent, calculate the present value of the bond.

Question 63

You borrow $30,000 for 10 years to pay tuition and fees.The annual interest rate is 12 percent.What monthly payment would be required to pay off the loan?

Question 64

On February 1, 2013, Janet buys a bond for $10,000 that makes coupon payments of $600 after each of the following two years and returns its principal of $10,000 at the end of the second year.In other words, it is a standard coupon bond with a 6 percent annual interest rate making payments once each year.
On February 1, 2014, Janet receives her first coupon payment of $600.At that time, the market interest rate on bonds like hers has fallen to 4 percent.She sells her bond to Justin at that time, for a price equal to the present value of the bond's payments.
a.How much does Justin pay Janet for the bond?
Both Janet and Justin have tax rates of 30 percent on interest income and 20 percent on capital gains.(Note that if someone has a capital loss, you may assume that he or she can reduce taxes by the amount of the capital loss times the tax rate of 20 percent.)

b.CalculateCalculate Janet's after-tax rate of return for the past year (from Feb. 1, 2013, to Feb. 1,2014).
Janet's after-tax rate of return for the past year (from Feb.1, 2013, to Feb.1,
2014).

c.What is Justin's after-tax rate of return for the year from Feb.1, 2014, to Feb.1, 2015?
Explain and show all your work for each part.You may assume, of course, that the market works and does not malfunction.

Question 65

Consider a coupon bond that pays $150 every year and repays its principal amount of $2,000 at the end of six years.
If the annual rate of discount is 7.5 percent, what is the present value of the bond?