ECON 2221 Ch.4

You are considering purchasing a home. You find one that you like but you realize that you will need to obtain a mortgage for $100,000 (PV). The mortgage company presents you with two options: a 15-year mortgage at a 6.0% annual rate and a 30-year mortgage at a 6.5% annual rate. What will be the fixed annual payment for each mortgage?

A. 10,296.28 B. 7,657,.74

Mary deposits funds into a CD at her bank. The CD has an annual interest of 4.0%. If Mary leaves the funds in the CD for two years she will have $540.80. What amount is Mary depositing? Assuming no penalties for withdrawing the funds early, what amount would Mary have at the end of one year?

A. 500 B. 520

Which one of the following best expresses the payment a saver receives for investing her money for two years? A) PV + PV B) PV + PV (1 + i) C) PV(1 + i)2 D) 2 PV(1 + i)

C) PV(1 + i)2

If a lender wants to earn a real interest rate of 3% and expects inflation to be 3%, they should charge a nominal interest rate that equals A) at least 0%. B) less than 6%. C) at least 6%. D) at least 7%. E) more than 7%.

C) at least 6%.

Which investment plan will provide the highest future value: $500 invested at 5 percent annually for four years and then that balance invested at 7 percent annually for an additional three years, or $500 invested at 6 percent annually for seven years?

$500 invested for four years at 5 percent interest and then that balance invested at 7% for three additional years will produce a balance of $744.52 at the end of seven years. The future value of $500 invested for seven years at 6 percent interest is $751.82.

An investment grows from $2,000 to $2,750 over the period of 10 years. What average annual growth rate will produce this result?

3.24%

Suppose Peter borrows $4,000 for one year from his friend John who charges Peter 7% interest. At the end of the year Peter will have to repay John how much money?

4,280

Calculate the internal rate of return for a machine that costs $500,000 and provides annual revenue of $115,000 per year for 5 years. You can assume all revenue is received once a year at the end of the year.

4.85%

A saver knows that if she put $95 in the bank today she will receive $100 from the bank one year from now, including the interest she will earn. What is the interest rate she is earning?

5.26%

A lender is promised a $100 payment (including interest) one year from today. If the lender has a 6% opportunity cost of money, they should be willing to accept what amount today?

94.34

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 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.

If a business owner is considering whether to borrow money to purchase a new machine that generates a stream of revenue over time, the decision process involves two primary steps. Which one of the following best summarizes the two steps? A) Calculate the internal rate of return on the investment in the machine and then compare that return to the cost of buying the machine. B) Calculate the internal rate of return on the investment in the machine and then calculate whether the stream of revenue covers the payments on the loan. C) Find out if the bank will approve the loan and then calculate the internal rate of return on the investment in the machine. D) Secure venture capital to finance the purchase of the machine and then pay dividends from the revenue stream generated.

A) Calculate the internal rate of return on the investment in the machine and then compare that return to the cost of buying the machine.

A bond offers a $50 coupon, has a face value of $1,000, and has 10 years to maturity. If the interest rate is 4.0% what is the value of this bond?

A) FV =1000, I/R = 4%, N=10, PMT= 50

Present value is higher when the future value of the payment is A) higher, the time until payment is shorter, and the interest rate is lower. B) lower, the time until payment is shorter, and the interest rate is higher. C) higher, the time until payment is longer, and the interest rate is lower. D) lower, the time until payment is shorter, and the interest rate is higher.

A) higher, the time until payment is shorter, and the interest rate is lower.

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. D) the total amount of interest payments made on a bond as a percentage of the amount borrowed.

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

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 that 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%.

A credit card that charges a monthly interest rate of 1.5% has an effective annual interest rate of A) 18.0%. B) 19.6%. C) 15.0%. D) 17.50%.

B) 19.6%.

Suppose that Stephen Curry, a basketball player for the Golden State Warriors, will become a free agent at the end of this NBA season. Suppose that Curry is considering two possible contracts from different teams as shown in the table. Note that the salaries are paid at the end of EACH year. The interest rate is 10%. Based on this information, which one of the statements below is true? Contract #1 (Boston) Contract #2 (Portland) Signing bonus (paid today) $1 million, $1 million First-year salary $2 million ,$4 million Second-year salary $4 million, $4 million Third-year salary $5 million, $3 million A) Curry should take the Boston contract because it has a higher present value. B) Curry should take the Portland contract because it has a higher present value. C) Curry is indifferent between the two contracts because they are both worth $12 million. D) Curry is indifferent between the two contracts because they are both worth $10.9 million.

B) Curry should take the Portland contract because it has a higher present value.

How does compound interest make your money "work for you"? A) It provides an interest deduction when you pay your loan off early. B) You earn interest on interest in addition to interest on principal. C) It provides an interest deduction if you take out a loan for longer than one year. D) It provides higher interest rates on larger loans with longer time horizons.

B) You earn interest on interest in addition to interest on principal.

The present value (PV) and the interest rate (R) have A) a direct relationship; as R increases, PV increases. B) an inverse relationship; as R increases, PV decreases. C) an unclear relationship; whether it is direct or inverse depends on the interest rate. D) no relationship.

B) an inverse relationship; as R increases, PV decreases.

Which one 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 sum of coupon payments. D) The price is the sum of the present value of the coupon payments and the present value of the face value.

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

It is important to understand present value and future value when studying financial markets because these tools ________________. A) are useful for evaluating risk. B) tell us how to invest in the stock market. C) are useful for analyzing the benefits of hedging investments. D) help us compare the value of a payments made at different points in time.

D) help us compare the value of a payments made at different points in time.

Ceteris paribus, which increases as interest rates rise—present value or future value? A) both B) neither C) only present value D) only future value

D) only future value

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.

D) pays a variable coupon rate depending on the bond's price.

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.

Briefly discuss the relationship between present value and each of the following. a) future value b) time c) interest rate

Holding time and interest rate constant, any percentage change in the future value will cause the same percentage change in the present value. Holding the future value and the interest rate constant, and increase in the time until payment reduces the present value and any decrease in time increases the present value. Holding future value and time constant, an increase in the interest rate reduces the present value and a decrease in the interest rate increases the present value.

Under which conditions do the future value become higher? Higher or lower the present value? Shorter or longer the investment horizon? Higher or lower the interest rate?

higher PV, the time until payment is longer, and the interest rate is high.

How much will the individual need to have saved by the time he or she is 65 if he or she plans on spending $40,000 per year while retired? An individual is currently 30 years old, wants to work until the age of 65, and expects to live till the age of 85. How much does she need to save (invest) annually before she retires? You can assume the individual can earn an interest rate of 5.0% and the $40,000 is in addition to any Social Security that may be received.

i. Solve for PV 1. N=20, I/R=5, PMT= 40,000 2. PV= 498,488 i. FV= 498,488 ii. N=35, I/R=5% iii. Calculate payment = 5,519 annual pmt

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.

reduces the present value.