A carry trade is a trading strategy that involves borrowing at a low interest rate and investing in an asset that provides a higher rate of return, hoping to turn a profit. A major currency pair is dollar-yen, quoted in Yen per $1. Suppose the current price is 82.10 Yen/$. Suppose also that the five-year dollar interest rate is 2.17% (compounded semi-annually, 30/360 daycount) and the five-year yen rate is 0.63% (compounded semi-annually, 30/360 daycount).

(a) Calculate the forward price for dollar-Yen five years forward.

(b) Suppose you went long one five-year forward contract from (a) above with the delivery price equal to the forward price. You are investing in a high-interest currency, the dollar, and borrowing a low-interest currency, the Yen, hoping to earn a profit in Yen when you convert the dollar back to yen in the future. Three years from now the FX rate is still 82.10 Y/$ and the two-year dollar rate is 0.78% and the two-year Yen rate is 0.41%. Find the value of the forward contract at that time. What is your profit or loss on the forward contract after three years?