Which formula best represents the forward exchange rate when adjusting for interest rate differentials?

• A. Spot rate × (1 + quote currency short term rate) ÷ (1 + base currency short term rate)
• B. Spot rate × (1 + base currency short term rate) ÷ (1 + quote currency short term rate)
• C. Spot rate + forward premium
• D. Forward rate equals spot rate

Answer: (A)

The key idea is that forward rates reflect the interest rate difference between the two currencies (covered interest parity). To lock in a future exchange, you must offset the return you would get from investing in one currency with the return you would get from investing in the other, after converting back at the forward date.

For a one-period horizon, the forward rate is calculated by adjusting the spot rate by the ratio of the interest accrued in the quote currency to the interest accrued in the base currency. In formula terms, F = S × (1 + i_quote) ÷ (1 + i_base). This means you multiply the current spot rate by (1 + the short-term rate of the quote currency) and divide by (1 + the short-term rate of the base currency). The result captures how much of the quote currency you’d need in the future to equal the future value of investing in the base currency, and vice versa.

So the correct formula aligns with the idea that the forward moves in relation to the interest differential, not by simply adding a premium to the spot or leaving it unchanged. The other forms either ignore compounding (adding a premium) or invert the relationship between the currencies (which would misstate how each currency’s rate affects the forward).