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# Bond Yield and Duration

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Assume coupons are paid annually. Here are the prices of three bonds with 10-year maturities:

Bond Coupon (%) Price (%)
2 81.62
4 98.39
8 133.42
________________________________________

a. What is the yield to maturity for each bond? (Round to 1 decimal place.)

Bond Coupon (%) YTM
2 %

4 %

8 %

________________________________________

b. Which bond offered the highest yield to maturity?

2% coupon bond

4% coupon bond

8% coupon bond

c. Which bond offered the lowest yield to maturity?

8% coupon bond

2% coupon bond

4% coupon bond

d-1. Which bond had the longest duration?

2% coupon bond

4% coupon bond

8% coupon bond

d-2. Which bond had the shortest duration?

2% coupon bond

4% coupon bond

8% coupon bond

#### Solution Summary

Excel spreadsheet attached answers multiple questions on bond yield, duration and coupons with calculations visible by selecting cells.

\$2.19

## What is the current price of each bond? b) If the market interest rate suddenly rises to 14% per year (effective annual yield), what will be the price of each of these bonds? Calculate the price and duration of each bond if the market interest rate is 10% per annum (effective annual yield).

1) Consider three zero coupon \$1000 face value bonds. Bond A matures 1 year from today. Bond B matures 5 years from today. Bond C matures 10 years from today. The current market interest rate is 11% per year (effective annual yield).
a) What is the current price of each bond?
b) If the market interest rate suddenly rises to 14% per year (effective annual yield), what will be the price of each of these bonds?

2) Consider two four-year bonds. Each bond has a face value of \$1000. Bond A pays an annual coupon of 7%, and Bond B pays an annual coupon of 11%.
a) Calculate the price and duration of each bond if the market interest rate is 10% per annum (effective annual yield).
b) Calculate the price of each bond if the market interest rate is 7% per annum (effective annual yield).
c) Which bond do you expect experienced the greatest percentage change in price?
d) What is the percentage cnage in the price of each bond?

3) What is the current price of this bond: face value of \$40,000, matures in 20 years. The bond makes no payments for the first six years, pays \$2000 semiannually for the subsequent eight years, and finally pays \$2500 semiannually for the last six years.

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