Consider a bond that promises the following cash flows. The yield to maturity is $12\%.$

You plan to buy this bond, hold it for $2\mathrm{.}5$ years, and then sell the bond.

a$.$ What total cash will you receive from the bond after the $2\mathrm{.}5$ years? Assume that periodic cash

flows are reinvested at $12\%.$

b$.$ If immediately after you buy this bond, all market interest rates drop to $11\%($including your

reinvestment rate$),$ what will be the impact on your total cash flow after $2\mathrm{.}5$ years? How does this compare to part $(a)?$

c$.$ Assuming all market interest rates are $12\%,$ what duration of this bond?