Consider a $10-$year zero$-$coupon bond that yields $6\%$ APR.

a$.$ What is the bond$$s modified duration?

b$.$ If the bond$$s convexity is $98\mathrm{.}9726,$ forecast the percent change in price for an interest rate

decrease of $2\%$ APR.

c$.$ Calculate the actual percent change in price for an interest rate decrease of $2\%.$

d$.$ Compare and explain your response from part b to that of part c$.$