Consider a five$-$year, $$1,000$ bond that pays a semi$-$annual coupon of $10$ percent. a$.$ What is the duration of the coupon bond if the current yield$-$to$-$maturity $($R$)$ is $14$ percent? b$.$ How would an increase in the current yield to maturity affect the duration of this coupon bond? c$.$ What is the expected change $($based on the duration calculated in part $$a$)$ in the price of the bond if yields were to rise by $50$ basis points from $14$ to $14\mathrm{.}5$ percent? d$.$Is the duration projected price change in $$c$$ bigger or smaller than the true change in the bond price?$$ Why? e$.$Suppose that you can buy in the market a one$-$year zero coupon bond and you have a three$-$year investment horizon. What proportion of your capital you have to invest in the five$-$year and the one$-$year bonds in order to immunize your investment against interest rate risk?