Deck 6: Measuring and Calculating Interest Rates and Financial Asset Prices

Question 1

Using the yield-approximation formula discussed in your text, determine the average annual yield on a bond whose current price is $1,100, par value is $1,000, coupon rate is 12 percent and whose term to maturity is ten years. Your answer is (to the nearest tenth of a percent):

A) 10.5 percent
B) 11 percent
C) 11.5 percent
D) 12 percent
E) 12.5 percent

Answer 1

10.5 percent

Question 2

What is different about interest rates or the price of credit, from other prices in the economy?

Answer 2

This price is unique because it is really a ratio of two quantities: the total required fee a borrower must pay a lender to obtain the use of credit for a stipulated time period divided by the total amount of credit made available to the borrower.

Question 3

What exactly is a basis point? Why is it an important interest-rate measure?

Answer 3

A basis point is 1/100 of a percent and is used for reporting small changes in interest rates.

Question 4

What assumptions underlie the calculation of the yield to maturity?

Question 5

See if you can explain the meaning of the following terms and, where a formula is involved, explain the components of each formula:

Question 6

How is the monthly payment that a home mortgage borrower must meet determined? Why is it that payments made early in the life of a typical home mortgage go largely to pay interest rather than repay principal?

Question 7

Suppose a 10-year bond is issued with a coupon rate of 8 percent when the market rate of interest is also 8 percent and the future market rate rises to 9 percent, what happens to the price of this bond? What happens to the bond's price if the market rate falls to 6 percent? Explain why?

Question 8

An AAA-rated corporate bond has a current market price of $800 and will pay $100 in interest for ten years. If its par value is $1,000, what is its yield to maturity?

Question 9

You plan to borrow $2,000 in order to take a vacation and want to repay the loan in a year. The banker offers you a simple interest rate of 12% with repayments in equal installments six months and twelve months from now. What is your total interest bill?

Question 10

An investor is interested in purchasing a new 20-year government bond carrying a 10 percent coupon rate. The bond's current market price is $875 for a $1,000 par value instrument. If the investor buys the bond at the going price and holds to maturity, what will be his yield to maturity?

Question 11

You discover a $1,000 par value bond just issued by XYC Corporation that pays interest semiannually at a coupon rate of 12 percent. The bond will mature in 10 years and can be purchased today at a price of $900 including the broker's commission. What is the bond's yield to maturity if all payments are made on time?

Question 12

You borrow $2,500 for five years at a rate of 12 percent per annum, compounded annually. What is the lump sum amount due at the end of the 5 years? What is the total amount of interest owed?

Question 13

In problem 7 above, if interest were compounded monthly, instead of annually, what lump sum amount would be due in five years and how much total interest must be paid?

Question 14

You have just placed $1,500 in a bank savings deposit and plan to hold that deposit for eight years, earning 5-1/2 percent per annum. If the bank compounds interest daily, what will be the total value of the deposit in eight years? How does your answer change if the bank switches to monthly compounding? Quarterly compounding?

Question 15

You decide to take out a 30-year mortgage loan to buy the home of your dreams. The home's purchase price is $120,000. You manage to scrape together a $20,000 down payment and plan to borrow the balance of the purchase price. Hardy Savings and Loan Association quotes you a fixed annual loan rate of 12 percent. What will your monthly payment be?

Question 16

A home mortgage loan for $60,000 is available from the neighboring bank at an interest rate of one percent per month. The loan will mature in 25 years. What payment must the borrower make each month under the terms of this loan agreement?

Question 17

A depositor leaves her funds in the amount of $5,000 in a credit union deposit for a full year but then withdraws $1000 after 270 days. At the end of the year the credit union pays her $300 in interest. What is this depositor's daily average balance and APY?

Question 18

A commercial loan extended to CIBER-LAND Corporation for $2.5 million assesses an interest charge of $350,000 up front. Using the discount method of calculating loan rates, what is the effective interest rate on this loan? Suppose that instead of deducting the interest owed up front the company's lender agrees to extend the full $2.5 million and add the amount of interest owed to the face of CIBER's note. What then is the loan's effective interest rate?