consider a 6x12 fra where the underlying six-month period is 183 days and the notional is $100. The fra fixed rate is 5%. At maturity of the contract the underlying libor for six months is 7%. What is the settlement amount of the FRA? Assume the actual/360 convention

0.9817

To calculate the settlement amount of the FRA, we need to understand the concept of a Forward Rate Agreement (FRA) and how it works.

A Forward Rate Agreement is a financial contract between two parties where they agree to exchange a fixed interest rate for a floating interest rate based on a specified notional amount over a predetermined period in the future. In this case, the FRA has a notional amount of $100 and a six-month period.

The fixed rate is agreed upon at the start of the contract and does not change throughout the agreement. In this case, the fixed rate is 5%.

LIBOR (London Interbank Offered Rate) is a benchmark interest rate that indicates the average interbank interest rate at which banks can borrow from one another. LIBOR rates are available for various tenors, including the six-month rate.

Given that the underlying LIBOR for six months is 7%, we can calculate the settlement amount using the following formula:

Settlement Amount = Notional Amount * (Floating Rate - Fixed Rate) * (Days/Year) / (1 + Floating Rate * (Days/Year))

Let's plug in the values:

Notional Amount = $100
Floating Rate = 7%
Fixed Rate = 5%
Days = 183
Year = 360 (actual/360 convention)

Settlement Amount = $100 * (0.07 - 0.05) * (183/360) / (1 + 0.07 * (183/360))

Simplifying the calculation:

Settlement Amount = $100 * 0.02 * 0.50833 / (1 + 0.35)

Now, calculate:

Settlement Amount = $1.017

Therefore, the settlement amount of the FRA is $1.017.