Lani, a trader in New York, has $$1$ million to trade with and the following

information: The current spot exchange rate is $106\mathrm{.}00$ Yen per USD, the $1-$year

forward rate is Yen$102\mathrm{.}5/$$; the US $ rate is $4\mathrm{.}00\%$ per annum, and the Yen

interest rate is $2\mathrm{.}00\%$ per annum. Suppose Lani is weighting the following two

trading strategies:

Strategy $1$: Simply keep the funds in a U$.$S$.$ bank for $1$ year to earn interests in

US$$,$

Strategy $2$: Convert US$ to Yen on the spot market then immediately save the

Yen to start earning the interest in Yen. Meanwhile, buy the appropriate amount

of $1-$year forward contract so that $1$ year later she can convert all the principal

and interest in Yen back to US$$.$

$(1)$ How much Lani will have one year later by following strategy $2?$

$(2)$ Suppose Lani has no capital at all, but she can borrow $1$ million US$ from a U$.$S$.$

lender by paying the lender current interest rates at $4\%.$ Is there a chance for

Covered Interest Arbitrage? If yes, how much is the profit?

$(3)$ Given the Yen interest rate remains at $2\mathrm{.}00\%,$ the current spot exchange rate

remains at Yen$106\mathrm{.}00/$$$,$ and the $1-$year forward rate remains at Yen$102\mathrm{.}5/$$$.$

According to the covered interest rate arbitrage formula, the U$.$S$.$ interest rate that

eliminates the covered interest rate arbitrage opportunity should be closest to the

level of: