You are thinking about entering into a $3$ year plain vanilla swap with annual payments and a notional principal of $$5,000,000.$ If you plan to pay the fixed rate on the swap what would you expect to pay if annual interest rates are listed below per annum with continuous compounding?

Year Rate

$13\mathrm{.}00\%$

$23\mathrm{.}50\%$

$34\mathrm{.}50\%$

A$)$ $$53,221\mathrm{.}46$

B$)$ $$150,000\mathrm{.}00$

C$)$ $$183,333\mathrm{.}33$

D$)$ $$227,411\mathrm{.}44$

E$)$ $$372,407\mathrm{.}89$

The answer is D$.$ Show all work to reach D$,$ no Excel.