Consider a four$-$year bond with a face value of $$100$ and a coupon rate of $10\%.$ The term structure of

interest rates is flat at $5\%($i$.$e$.$ yt $=5\%$ for all t$).$

a$.$ Calculate the duration of this bond, and use the duration rule to estimate the dollar change in price if the

term structure of interest shifts to $6\%?$

b$.$ What would the actual price change be$?$

c$.$ Explain the approximation error that arises from using duration rule by comparing the linear rule to the

actual price$-$yield relationship. What it the relationship between yield and duration?

d$.$ Assume yields instead shift rom $5\%$ to $4\%?$ Is the magnitude of the price change larger or smaller

compared to the shift from $5\%$ to $6\%$ in part a$?$ Explain why this occurs.