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Borrowing and lending in foreign currencies

Investing $1,000,000 for six months.
Alternatives:
Consider purchasing US T Bills at 1.810% (6 month rate, not annual), matures in 26 weeks.
Invest in Yen by converting dollars to Yen. Interest rate in Japan is 15%.

Spot Exchange Rate is $1.00/Yen100, six month forward rate is $1.00/Yes110,

Solution Preview

Spot rate = 100 Yen /$
Forward rate= 110 Yen /$

For no arbitrage condition (interest rate parity)
Forward / Spot = (1+ interest rate for 6 months in Japan) / (1+ interest rate for 6 months in US)

or
(110/100) x (1+ interest rate for 6 months in US) = (1+ interest rate for 6 months in Japan)

interest rate for 6 months in US= 1.81%

Therefore

(110/100) x (1+ 1.81%) = (1+ interest rate for 6 months in Japan)
or
(1+ interest rate for 6 months in Japan)= 1.11991
or
interest rate for 6 months in Japan= 0.11991 or 11.991%

Case: Interest rate in Japan= 11.991%

If the interest rate in Japan is 11.991% there is no arbitrage opportunity
Let us see why this is so
Start with $1,000,000
Borrow $1,000,000 for six months at an interest rate of 1.81%
Principal and interest on this amount to be returned after 6 months = $1,018,100 =1000000x(1+ 0.0181)

Convert $1,000,000 into Yen at the spot rate of 100 Yen /$
Amount in Yen received= ¥100,000,000 =(1000000x100)
Enter into a forward contract to convert Yen back to dollars at the end of 6 months at the forward rate of 110 Yen /$
Invest this amount at an interest rate of 11.991%
Principal and interest on this invested amount received after 6 months = ...

Solution Summary

Evaluates investment in Yen and dollar.

$2.19