A bank enters into a Forward Rate Agreement in which it agrees to pay the fixed rate f$3$m$,3$m $=2\mathrm{.}24209\%$

in three months in exchange for the market rate with the same term. If in three months the projected interest rate is set at $2\mathrm{.}15\%,$ an interest period of $90$ days and a nominal value of $100,000,000$ are assumed,

$($a$)$ Calculate the value of the contract at the end of the period.

$($b$)$ Obtain the value of the contract at the beginning of the period of interest.