finance

Your friend would like to know the price and duration of an annual coupon bond but she has lost her

financial calculator. You decide to help. The bond is a 4-year annual 7% coupon bond with a yield

to maturity of 9%. Determine the current price and the duration of the bond.

You know that your friend will not buy the bond immediately; instead, she plans to trade at the end

of the week. You worry that rates may change in the meantime and decide to perform additional

calculations.

In class, we learned that the duration rule for price sensitivity ( ) can tell you

how prices will differ when interest rates change. You also remember that this formula only works

well for small changes in rates. You decide to recalculate the bond’s price for two scenarios: 1) when

rates decrease by one basis point and 2) when rates decrease by one hundred basis points by the end

of the week. Price the bond in both cases using the duration formula for price sensitivity. To check

how well the formula works, re-price the bond in both cases using bond pricing instead. Describe

the magnitude of the error you find when using the duration formula across the two scenarios.