You have a $5-$year investment holding horizon, would like to earn a $6\%$ annual compound return each year, and you have a choice between two bonds. Whatever money $ you have to invest will be invested in one type of bonds or another.

Find the Bond Price, Duration and Modified Duration for each bond $($show your work and answer the questions below$)$

$$ Bond $1$ has a $6\%$ annual coupon rate, $$1000$ maturity value, n $=5$ years, YTM $=6\%($pays a $$60$ annual coupon at the end of each year and $$1,000$ maturity payment at maturity$).$ Each bond will be held to maturity.

$$ Bond $2$ is a zero$-$coupon bond with a $$1000$ maturity value, and n $=5$ years; YTM$=6\%($pays no coupons$)$; only a $$1,000$ maturity payment at maturity$).$

a$.$ Price Bond $1\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ Price Bond $2\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ Duration Bond $1\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ Duration Bond $2\_\_\_\_\_\_\_\_\_\_\_\_$

c$.$ Modified Duration Bond $1\_\_\_\_\_\_\_$ Modified Duration Bond $2\_\_\_\_\_\_\_\_\_\_\_\_$

$($Be sure to show your work for the bond price and duration calculations for credit$).$

d$.$ Which of the two bonds should you choose for your $5-$year investment horizon to duration match to ensure your desired $6\%$ annual compound return if you hold either bond to the end of $5$ years? Explain why. $($Assume the same default risk for each bond$).$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

e$.$ If interest rates go up by $1\%,$ what will be the $\%$ Change in the market value for each Bond$$s Price? $($Hint Change in Price $\%=-$ Modified Duration x Change in Rate $($expressed as a fraction, i$.$e$.\mathrm{.}01).$

$\%$ Change in Price for Bond $1\_\_\_\_\_\_\_\_\%$ Change in Price for Bond $2\_\_\_\_\_\_\_\_$

f$.$ Which of the $2$ bonds has more price risk, and which has more reinvestment risk?

Explain why.$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$