Suppose annual interest rates are 1% in Japan and 9% in New Zealand

Interest rate in Japan, r1 = 1%; Interest rate in New Zealand, r2 = 9%; time, t = 90 days = 1 quarter = 0.25 years

Let the current exchange rate be NZ $ E / Yen.

Your trade

• Borrow say NZ$ 100
• Convert into Yen = 100 / E = 100 / E
• Invest in Yen. Maturity proceeds in Yen = Invested amount x (1 + r1 x t) = 100/E x (1 + 1% x 0.25) = 100.25 / E
• Meanwhile the Japanese yen appreciates by 3%. hence the new exchange rate @ t = 90 days = E x (1 + appreciation rate) = E x (1 + 3%) = NZ $ 1.03E / Yen
• Hence, maturity proceeds when converted to NZ $ = Maturity proceeds in Yen x New exchange rate = 100.25 / E x 1.03E = NZ $ 103.26
• Meanwhile, maturity amount of the borrowed capital in NZ $ = Amount borrowed x (1 + r2 x t) = 100 x (1 + 9% x 0.25) = NZ $ 102.25

Hence, your profit = maturity proceeds when converted to NZ $ - maturity amount of the borrowed capital in NZ $ = 103.26 - 102.25 = NZ $ 1.01

Hence, we made a profit of

• NZ $ 1.01 for every NZ $ 100 invested in the carry trade
• Profit / investment = 1.10 / 100 = 1.01% in NZ $ terms