Suppose today $($Spot date$)$ is Friday October $4$th $,2024$ and interest rates for different maturities are as follows:

$1$ Month $5\mathrm{.}26\%$

$3$ Month $5\mathrm{.}23\%$

$6$ Month $5\mathrm{.}04\%$

$9$ Month $4\mathrm{.}58\%$

Use arbitrage pricing to determine the forward rate that starts in three months from today and matures in $9$ months from today? This is called Forward Rate Agreement or FRA $39$ where $3$ is the starting date from today and $9$ is the maturity date from today

If you are offered $39$ FRA at $3\%$ show that there is an arbitrage possibility and construct it$.$

If you are offered $39$ FRA at $6\mathrm{.}5\%$ show that there is an arbitrage possibility and construct it$.$

You are an importer of cars and receive $$10,000,000$ worth of car shipments in one month, at which time you have to pay for it by borrowing this amount from a bank and plan to pay it back in $5$ months. You want to fix the borrowing rate today.

What would be this rate?

How much will your interest payment be$?$

What is the total amount that you have to pay the bank?