The one-year forward exchange rate is Rupees 40/$. If the one-year interest rate in Australia is 4% and in India is 7%, what is the spot exchange rate so as to preclude arbitrage?

Question

Quizplus · Accepted Answer

Let us assume that we have $1,000 to invest. 
In Australia, after one year, we will have $1,040 (4% return). If we convert this to Indian Rupees at the current spot exchange rate (let's assume it is X), we will get 1,040X. 
Alternatively, we can convert $1,000 to Indian Rupees at the current spot exchange rate (let's assume it is Y), and invest it in India. After one year, we will have 1,070Y (7% return). Then, we can convert this back to USD at the forward exchange rate (40 rupees per dollar), and we will have 1,070Y/40. 
Since we want to preclude arbitrage, both of these options should yield the same amount of money. 
Therefore: 
1,040X = 1,070Y/40 
Solving for X, we get X = 38.88.

The One-Year Forward Exchange Rate Is Rupees 40