A financial institution has entered into an interest rate swap with company $x.$

Under the terms of the swap, it receives $4\%$ per annum and pays six$-$month LIBOR on a

principal of $$10$ million for four years. Payments are made every six months.

Suppose that company $x$ defaults on the sixth payment date $($end of year $3)$ when the

six$-$month forward LIBOR rates for all maturities are $3\%$ per annum.

Assume that six$-$month LIBOR was $3\mathrm{.}5\%$ per annum halfway through year $3$ and that at

the time of default all OIS rates are $2\mathrm{.}5\%$ per annum.

OIS rates are expressed with continuous compounding; other rates are expressed with

semiannual compounding.

The loss to the financial institution is closest to:

a$.$ $$123,144$

b$.$ $$469,433$

c$.$ $$592,578$

d$.$ $$246,288$