Q$3(9$ points$)$: Consider a bond that promises the following cash flows. The required discount rate is $12\%.$

$\backslash$table$[[$Year$,0,1,2,3,4],[$Promised Payments,,$160,170,180,230]]$

You plan to buy this bond, hold it for $2^{\frac{1}{2}}$ years, and then sell the bond.

a$.$ What total cash will you receive from the bond after the $2\frac{1}{2}$ years? Assume that periodic cash flows are reinvested at $12\%.$

b$.$ If all market interest rates drop to $11\%($including your reinvestment rate$)$ immediately after buying this bond, what will be the impact on your total cash flow after $2\frac{1}{2}\frac{?}{?}$ years? How does this compare to part $($a$)?$

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