A forward rate agreement $($FRA$)$ pays $4\mathrm{.}8\%$ interest $($quarterly compounded$)$ for $3$ months starting in $0\mathrm{.}5$ years on a principal of $$200$ million.

Consider the following annual interest rates:

Maturity $($years$)$ Risk$-$free

spot rate

$($with continous compounding$)3-$month

forward rate

$($with quarterly compounding$)$

$0\mathrm{.}250\mathrm{.}038-$

$0\mathrm{.}50\mathrm{.}040\mathrm{.}0422$

$0\mathrm{.}750\mathrm{.}0430\mathrm{.}0493$

$10\mathrm{.}0490\mathrm{.}0676$