You are running the FX trading desk at a large investment bank. You have the following rates

available to you:

Spot Dollar$/$Yen Exchange Rate $134\mathrm{.}89$ Yen$/$USD

$3-$month Forward Dollar$/$Yen Rate $133\mathrm{.}12$ Yen$/$USD

$3-$month US $($dollar$)$ Risk$-$free Interest Rate $5\mathrm{.}00\%$

Assume that there are no transaction costs, and that you can either buy or sell at these exchange

rates. Also, the interest rates above are quoted in annualized, continuously$-$compounded form,

and are the same for borrowing or lending. Please be aware that the future exchange rates are

quoted as the number of USD per unit of the foreign currency.

$($a$)$ What must the $3-$month Japanese $($yen$)$ interest rate $($annualized$,$ c$.$c$.)$ be for there to be no

arbitrage?

$($b$)$ Suppose that the annualized, continuously$-$compounded $3-$month Yen interest rate is $1\mathrm{.}0\%.$

Describe exactly what transactions you would undertake at these prices$/$rates to lock in an

arbitrage profit.