An investment manager wants to hedge $$60,000,000$ 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

$1506\mathrm{.}8\%$

$2707\mathrm{.}9\%$

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

b$.$ What is the price of an FRA expiring in $150$ days based on the $120-$day Euribor?

Suppose that $54$ days into the term of the FRA, $96$day Euribor is $6\mathrm{.}8\%$ and $216$day Euribor is $6\mathrm{.}72\%.$ Given a notional principal of $$60,000,000$ and the long position on the FRA:

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

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