An investment manager wants to hedge $$75,000,000$ against a possible adverse change in interest rates. She therefore plans to take a long position on an FRA that expires in $60$ days, based on a $150$day Euribor. The current term structure for Euribor is as follows:

t rt

$1506\mathrm{.}9\%$

$3007\mathrm{.}55\%$

a$.$ The FRA that the investment manager has most likely committed to is a$?$

$`5$x$5`$

$`5$x$15`$

$`5$x$10`$

$`10$x$5`$

b$.$ What is the price of an FRA expiring in $150$ days based on the $150-$day Euribor?

$\%$

Round your answer to two decimals.

Suppose that $55$ days into the term of the FRA, $95$day Euribor is $6\mathrm{.}21\%$ and $245$day Euribor is $6\mathrm{.}04\%.$ Given a notional principal of $$75,000,000$ and the long position on the FRA:

c$.$ What is the annualized rate applicable on a $150$day loan $20$ days from today?

$\%$

Round your answer to two decimals.

d$.$ What is the value of the FRA?

$

Round your answer to the dollar.