Zero-coupon bond with 20 years left to maturity A 10%, 20-year annual bond has a Macaulay duration of 10

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Zero-coupon bond with 20 years left to maturity

A 10%, 20-year annual bond has a Macaulay duration of 10.18 years.

Assume that the market interest rates are at 8 percent.

 

1. Calculate these bonds value at the current market interest rates. State whether the price of the bonds is sold at a premium, at par, or at a discount.
2. Using present value method, calculate the price of these bonds in one year if the market interest rates drop to 6.5%. What are the price changes in percentage?
3. Using Modified duration, by what percentage will the bond prices change if market interest rates drop to 6.5%?
4. Explain the difference in answer in parts (b) and (c).