Chapter 04 Future Value, Present Value and Interest Rates Part A

Which of the following best expresses the future value of $100 left in a savings account earning 3.5% for three and a half years? a. $100(1.035)^3.5 b. $100(0.35)^3.5 c. $100 × 3.5 × (1.035) d. $100(1.035)^3/2

a. $100(1.035)^3.5

The decimal equivalent of a basis point is: a. 0.0001 b. 1.00 c. 0.001 d. 0.01

a. 0.0001

The future value of $100 that earns 10% annually for n years is best expressed by which of the following? a. $100(0.1)^n b. $100 × n × (1.1) c. $100(1.1)^n d. $100/(1.1)^n

c. $100(1.1)^n

Which of the following best expresses the present value of $500 that you have to wait four years and three months to receive? a. ($500/4.25) × (1 + i) b. $500 × 4.25 × (1 + i) c. $500/(1 + i)^4.25 d. ($500/4) × (1 + i)^3

c. $500/(1 + i)^4.25

As inflation increases, for any fixed nominal interest rate, the real interest rate: a. also increases. b. remains the same, that's why it is real. c. decreases. d. decreases by less than the increase in inflation.

c. decreases.

A promise of a $100 payment to be received one year from today is: a. more valuable than receiving the payment today .b. less valuable than receiving the payment two years from now. c. equally valuable as a payment received today if the interest rate is zero. d. not enough information is provided to answer the question.

c. equally valuable as a payment received today if the interest rate is zero.

The future value of $200 that is left in account earning 6.5% interest for three years is best expressed by which of the following? a. $200(1.065) × 3 b. $200(1.065)/3 c. $200(1.065)^n d. $200(1.065)^3

d. $200(1.065)^3

Usually an investment will be profitable if: a. the internal rate of return is less than the cost of borrowing. b. the cost of borrowing is equal to the internal rate of return. c. it is financed with retained earnings. d. the cost of borrowing is less than the internal rate of return.

d. the cost of borrowing is less than the internal rate of return.

Doubling the future value will cause: a. the present value to fall by half. b. the interest rate, i, to double. c. no change to present value, only the interest rate. d. the present value to double.

d. the present value to double.

The coupon rate for a coupon bond is equal to the: a. annual coupon payment divided by the face value of the bond. b. annual coupon payment divided by the purchase price of the bond. c. purchase price of the bond divided by the coupon payment. d. annual coupon payment divided by the selling price of the bond.

a. annual coupon payment divided by the face value of the bond

The shorter the time until a payment the: a. higher the present value. b. lower the present value because time is valuable. c. lower must be the interest rate. d. higher must be the interest rate.

a. higher the present value.

If a lender wants to earn a real interest rate of 3% and expects inflation to be 3%, he/she should charge a nominal interest rate that: a. is at least 7%. b. is anything above 0%. c. equals the real rate desired plus expected inflation. d. equals the real rate desired less expected inflation.

a. is at least 7%.

If the internal rate of return from an investment is more than the opportunity cost of funds the firm should: a. make the investment. b. not make the investment. c. only make the investment using retained earnings. d. only make part of the investment and wait to see if interest rates decrease.

a. make the investment.

The "coupon rate" is: a. the annual amount of interest payments made on a bond as a percentage of the amount borrowed. b. the change in the value of a bond expressed as a percentage of the amount borrowed. c. another name for the yield on a bond, assuming the bond is sold before it matures.

a. the annual amount of interest payments made on a bond as a percentage of the amount borrowed.

Which of the following statements is most correct? a. We can always compute the ex post real interest rate but not the ex ante real rate. b. We cannot compute either the ex post or ex ante real interest rates accurately. c. We can accurately compute the ex ante real interest rate but not the ex post real rate. d. None of the statements are correct.

a. We can always compute the ex post real interest rate but not the ex ante real rate.

Suppose the nominal interest rate on a one-year car loan is 8% and the inflation rate is expected to be 3% over the next year. Based on this information, we know: a. the ex ante real interest rate is 5%. b. the lender benefits more than the borrower because of the difference in the nominal versus real interest rates. c. at the end of the year, the borrower pays only 5% in nominal interest. d. the ex post real interest rate 11%.

a. the ex ante real interest rate is 5%.

We should expect a country that experiences volatile inflation to also have: a. volatile nominal interest rates. b. volatile real interest rates but stable nominal rates. c. stable nominal interest rates. d. volatile real interest rates.

a. volatile nominal interest rates.

According to the rule of 72: a. any amount should double in value in 72 months if invested at 10%. b. 72/interest rate is the number of years approximately it will take for an amount to double. c. 72 × interest rate is the number of years it will take for an amount to double. d. the interest rate divided by the number of years invested will always equal 72%.

b. 72/interest rate is the number of years approximately it will take for an amount to double.

Considering the data on real and nominal interest rates for the U.S. from 1979 to 2012, which of the following statements is most accurate? a. The real interest rate remains unchanged over time. b. There have been times when the real interest rate has been negative. c. Nominal interest rates higher in 2000 than they had been at any other point in time. d. The inflation rate is always greater than the real interest rate.

b. There have been times when the real interest rate has been negative.

From the Fisher equation we see that the nominal interest rate and expected inflation have: a. an inverse relationship. b. a relationship which is direct but less than one-to-one. c. a relationship which is direct and one-to-one. d. no relationship

b. a relationship which is direct but less than one-to-one.

Interest rates that are adjusted for expected inflation are known as: a. coupon rates. b. ex ante real interest rates. c. ex post real interest rates. d. nominal interest rates.

b. ex ante real interest rates.

Credit: a. probably came into being at the same time as coinage. b. predates coinage by 2,000 years. c. did not exist until the middle ages. d. first became popular due to the writings of Aristotle.

b. predates coinage by 2,000 years.

A coupon bond is a bond that: a. always sells at a price that is less than the face value. b. provides the owner with regular payments. c. pays the owner the sum of the coupons at the bond's maturity. d. pays a variable coupon rate depending on the bond's price.

b. provides the owner with regular payments.

Higher savings usually requires higher interest rates because: a. everyone prefers to save more instead of consuming. b. saving requires sacrifice and people must be compensated for this sacrifice. c. higher savings means we expect interest rates to decrease. d. of the rule of 72.

b. saving requires sacrifice and people must be compensated for this sacrifice.

Compound interest means that: a. you get an interest deduction for paying your loan off early. b. you get interest on interest. c. you get an interest deduction if you take out a loan for longer than one year. d. interest rates will rise on larger loans.

b. you get interest on interest.

Which of the following best expresses the proceeds a lender receives from a one-year simple loan when the annual interest rate equals i? a. PV + i b. FV/i c. PV(1 + i) d. PV/i

c. PV(1 + i)

Which of the following best expresses the payment a saver receives for investing their money for two years? a. PV + PV b. PV + PV (1 + i) c. PV(1 + i)^2 d. 2PV(1 + i)

c. PV(1 + i)^2

Which of the following best expresses the payment a lender receives for lending money for three years? a. 3PV b. PV/(1+i)^3 c. PV/(1 + i)^3 d. FV/ (1 + i)^3

c. PV/(1 + i)^3

The price of a coupon bond will increase as the: a. face value decreases. b. yield increases. c. coupon payments increase. d. term to maturity is shorter.

d. term to maturity is shorter.

An investment carrying a current cost of $120,000 is going to generate $50,000 of revenue for each of the next three years. To calculate the internal rate of return we need to: a. calculate the present value of each of the $50,000 payments and multiply these and set this equal to $120,000. b. find the interest rate at which the present value of $150,000 for three years from now equals $120,000. c. find the interest rate at which the sum of the present values of $50,000 for each of the next three years equals $120,000. d. subtract $120,000 from $150,000 and set this difference equal to the interest rate.

c. find the interest rate at which the sum of the present values of $50,000 for each of the next three years equals $120,000.

A mortgage, where the monthly payments are the same for the duration of the loan, is an example of a(n): a. variable payment loan. b. installment loan. c. fixed payment loan. d. equity security.

c. fixed payment loan.

A change in the interest rate: a. has a smaller impact on the present value of a payment to be made far into the future than on one to be made sooner. b. will not make a difference in the present values of two equal payments to be made at different times. c. has a larger impact on the present value of a payment to be made far into the future than on one to be made sooner. d. has a larger impact on the present value of a bigger payment to be made far into the future than on one of lesser value.

c. has a larger impact on the present value of a payment to be made far into the future than on one to be made sooner.

The lower the interest rate, i, the: a. lower is the present value. b. greater must be n. c. higher is the present value. d. higher is the future value.

c. higher is the present value.

If a saver has a positive rate of time preference then the present value of $100 to be received 1 year from today is: a. more than $100. b. not calculable. c. less than 100. d. unknown to the saver.

c. less than 100.

At any fixed interest rate, an increase in time, n, until a payment is made: a. increases the present value. b. has no impact on the present value since the interest rate is fixed. c. reduces the present value. d. affects only the future value

c. reduces the present value.

The price of a coupon bond is determined by: a. taking the present value of the bond's final payment and subtracting the coupon payments. b. taking the present value of the coupon payments and adding this to the face value. c. taking the present value of all of the bond's payments. d. estimating its future value.

c. taking the present value of all of the bond's payments.

The internal rate of return of an investment is: a. the same as return on investment. b. zero when the present value of an investment equals its cost. c. the interest rate that equates the present value of an investment with its cost. d. equal to the market rate of interest when an investment is made.

c. the interest rate that equates the present value of an investment with its cost.

The interest rate that equates the price of a bond with the present value of its payments: a. will vary directly with the value of the bond. b. should be the one that makes the value equal to the par value of the bond. c. will vary inversely with the value of the bond. d. should always be greater than the coupon rate.

c. will vary inversely with the value of the bond.

A borrower who makes a $1,000 loan for one year and earns interest in the amount of $75, earns what nominal interest rate and what real interest rate if inflation is two percent? a. A nominal rate of 5.5% and a real rate of 2.0%. b. A nominal rate of 7.5% and a real rate of 5.0%. c. A nominal rate of 7.5% and a real rate of 9.5%. d. A nominal rate of 7.5% and a real rate of 5.5%.

d. A nominal rate of 7.5% and a real rate of 5.5%.

Which of the following is necessarily true of coupon bonds? a. The price exceeds the face value. b. The coupon rate exceeds the interest rate. c. The price is equal to the coupon payments. d. The price is the is the sum of the present value of coupon payments and the face value.

d. The price is the is the sum of the present value of coupon payments and the face value.

The price of a coupon bond is determined by taking the present value of: a. the bond's final payment and subtracting the coupon payments. b. the coupon payments and adding this to the face value. c. the bond's final payment. d. all of the bond's payments.

d. all of the bond's payments.

Compounding refers to the a. calculation of after tax interest returns. b. internal rate of return a firm earns on an investment. c. real interest return after taxes. d. process of earning interest on both the principal and the interest of an investment.

d. process of earning interest on both the principal and the interest of an investment.