# Bond price changes; holding period yield; bank discount rate

Suppose a 10-year bond is issued with an annual coupon rate of 8 percent when the market rate of interest is also 8 percent. If the 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.

An investor is interested in purchasing a new 20-year government bond carrying a 10 percent annual coupon rate with interest paid twice a year. 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 or her yield to maturity? Suppose the investor sells the bond at the end of 10 years for $950. What is the investor's holding-period yield?

Calculate the bank discount rate of return (DR) and the YTM-equivalent return for the following money market instruments:

A. Purchase price, $96; par value, $100; maturity, 90 days.

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#### Solution Summary

The solution answers questions related to Bond price changes; holding period yield; bank discount rate of return, YTM return,

Investment questions: nominal annual return, effective annual rate, bond's market price, one-year interest rate expected one year from now, duration of a five-year bond, decrease in the market rates of interest, discount quote, commercial paper, T-Bill, annuity, mortgage, foreign exchange rate, ARM, fixed rate mortgages

Assume all bonds have a face value of $1,000.00, unless otherwise informed

1. You buy an investment today for $9,825. You sell the investment in 90 days for $10,000.

a. What is the nominal annual return on this investment?

b. What is the effective annual rate on this investment?

2. A 10 year semi-annual payment corporate coupon bond has a coupon rate of 11% and a required return of 10%. The bond's market price is

3. Suppose we look in the newspaper and find the following rates: the rate on 1-year securities is 4.65%, on a similar 2-year security 6.30%, and a 3-year security 6.67%. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now?

4. Consider the following bonds:

a. What is the duration of a five-year bond with a 6.5 percent semiannual coupon if the yield to maturity (ytm) is 7.00%?

b. What is the duration of a 20-year zero coupon bond with a yield to maturity of 7.65%

c. You expect a sudden, but widely unanticipated, decrease in the market rates of interest due to a change in position by the Federal Reserve. Would you rather be holding in your asset portfolio the bond from a. above (BOND A) or the zero from b. above (BOND B)? Which bond would you prefer, and why?

5. If a $10,000 par T-Bill has a 4.5% discount quote and a 180 day maturity, what is the price of the T-Bill?

6. Ninety day commercial paper can be bought at a 4% discount. What are the bond equivalent yield and the effective annual rate on the commercial paper?

a. Why do these rates differ?

7. You purchase a $200,000 house and you pay 20% down. You obtain a fixed rate mortgage where the annual interest rate is 7% and there are 360 monthly payments. What is the monthly payment?

8. A Swiss bank converted 1 million Swiss francs to euros to make a euro loan to a customer when the exchange rate was 1.75 francs per euro. The borrower agreed to repay the principle plus 4% interest in 1 year. The borrower repaid euros at loan maturity and when the loan was repaid the exchange rate was 1.85 francs per EURO. What was the bank's franc rate of return?

9. At the beginning of the year the exchange rate between the Brazilian Real and the U.S. dollar is 2.5 Reals per dollar. Over the year Brazilian inflation is 16% and U.S. inflation is 2%. If purchasing power parity holds, at year end the exchange rate should be _____ dollars per real.

10. Why do mortgage lenders prefer ARMs while many borrowers prefer fixed rate mortgages, ceteris paribus?

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