If rF and rD are the interest rates of a foreign country and domestic country, respectively, and if SF/D and fF/D are spot exchange rate and forward exchange rate between the countries F and D, the interest rate parity is indicated by :
\( \dfrac{(1 + r_F)}{(1 + r_D)} = \dfrac{f_{F/D}}{S_{F/D}} \)
Option 3 is correct: \( \dfrac{(1 + r_F)}{(1 + r_D)} = \dfrac{f_{F/D}}{S_{F/D}} \).
Interest Rate Parity (IRP) is a no-arbitrage condition connecting interest rates in two countries with their spot and forward exchange rates. It says an investor should earn the same hedged return whether funds are invested at home or abroad; otherwise covered-interest arbitrage would eliminate the difference.
With the quote written as units of F per unit of D, investing at the foreign rate grows funds by \( (1 + r_F) \) while investing domestically grows them by \( (1 + r_D) \). To compare, the foreign proceeds must be converted back through the forward rate, giving the parity relation:
\( \dfrac{1 + r_F}{1 + r_D} = \dfrac{f_{F/D}}{S_{F/D}} \)
Thus the country with the higher interest rate trades at a forward discount, and the currency with the lower rate trades at a forward premium — exactly cancelling the interest advantage.
Why the others are wrong: Option 1 inverts the interest-rate ratio; Option 2 pairs the correct interest ratio with an inverted (S/f) exchange ratio; Option 4 is ruled out because Option 3 is a valid form of IRP.
Takeaway: Interest ratio (F over D) equals the forward-to-spot ratio — the essence of covered interest parity.
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