# Duration of bond

Calculate the duration of an 8 percent, $1,000 par bond that matures in the three years if the bond's YTM is 10 percent and interest is paid semi-annually.

a) Calculate this bond's modified duration.

b) Assuming the bond's YTM goes from 10 percent to 9.5 percent, calculate an estimate of the price change.

Please show the work. Excel spreadsheet would be great.

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#### Solution Preview

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Calculate the duration of an 8 percent, $1,000 par bond that matures in the three years if the bond's TYM is 10 percent and interest is paid semiannually.

?In general, for a bond paying constant periodic coupons, the formula for Macaulay's Duration is:

?In the formula, C is the annual coupon rate, M is the bond maturity (in years), and YTM is the yield to maturity, n is the compounding frequency (i.e. n=1 for annual 2 for semiannual , 4 for quarterly) ...

#### Solution Summary

Calculates duration, modified duration and price change when interest rate changes.