Assume a five$-$year bond with a face value of $$1,000$ that pays a $6\%$ coupon $($annual coupon payment$)$ with a yield to maturity $($YTM$)$ of $5\%.$

a$)$ Calculate Macaulay duration and discuss your result.

b$)$ Calculate Modified duration and discuss your result.

c$)$ Calculate Duration$-$adjusted price change $($in $\%$ and $ value$)$ if YTM increases from $5\%$ to $7\%.$

d$)$ Explain why modified duration is the better measure than maturity when calculating the bond$$s sensitivity to changes in interest rates.

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