Mathematically, interest rate parity between the currencies of two countries, A and B, can be expressed as ________.

Question

Quizplus · Accepted Answer

Mathematically, the uncovered interest rate parity can be expressed as:
$$
(1 + i_A) = \frac{F}{S} (1 + i_B)
$$
Where:
- $i_A$ is the interest rate in country A.
- $i_B$ is the interest rate in country B.
- $S$ is the current spot exchange rate (the amount of country A's currency needed to buy one unit of country B's currency).
- $F$ is the forward exchange rate agreed upon today for a certain time in the future.
However, the options provided in the question seem to be a mix of incorrect formulas. The correct formula for uncovered interest rate parity is not listed among the options. The closest option to the correct formula is:
D) $I(1 + i_A) = \left(\frac{1}{S}\right)(1 + i_B) F$
This option represents the relationship between the interest rates and the exchange rates, assuming $I$ is the initial investment amount. However, the use of $I$ in this context is not standard, and the formula typically does not include an initial investment amount when expressing the interest rate parity condition.
Therefore, the full answer for the input question, based on the standard formula for uncovered interest rate parity, is:
D) $I(1 + i_A) = \left(\frac{1}{S}\right)(1 + i_B) F$

Mathematically, Interest Rate Parity Between the Currencies of Two Countries I(1+iB)=(1 S)(1−iA)F\mathrm{I}(1+\mathrm{i} \mathrm{B})=\left(\frac{1}{\mathrm{~S}}\right)(1-\mathrm{i} \mathrm{A}) \mathrm{F}I(1+iB)=( S1​)(1−iA)F

Mathematically, Interest Rate Parity Between the Currencies of Two Countries $\mathrm{I}(1+\mathrm{i} \mathrm{B})=\left(\frac{1}{\mathrm{~S}}\right)(1-\mathrm{i} \mathrm{A}) \mathrm{F}$