Question

The one-year risk-free rate in the U.S. is 2.580 percent and the one-year risk-free rate in Mexico is 4.22 percent. The one-year forward rate between the Mexican peso and the U.S. dollar is MXN12.223 per $. What is the spot exchange rate? Assume interest rate parity holds.


Multiple Choice

MXN13.901 per $


MXN12.223 per $


MXN12.418 per $


MXN14.871 per $


MXN12.031 per $

Answer 1

To find the spot exchange rate using interest rate parity, we can use the following formula:

\[
\frac{F}{S} = \frac{(1 + r_d)}{(1 + r_f)}
\]

Where:
- \(F\) = forward exchange rate (MXN per $)
- \(S\) = spot exchange rate (MXN per $)
- \(r_d\) = domestic risk-free interest rate (Mexico)
- \(r_f\) = foreign risk-free interest rate (U.S.)

Given the data:
- \(F = 12.223\) MXN per $
- \(r_d = 4.22\% = 0.0422\)
- \(r_f = 2.580\% = 0.0258\)

Rearranging the formula to solve for the spot exchange rate \(S\):

\[
S = \frac{F}{\frac{(1 + r_d)}{(1 + r_f)}}
\]

Substituting the known values:

\[
S = \frac{12.223}{\frac{(1 + 0.0422)}{(1 + 0.0258)}}
\]

Calculating \(1 + r_d\) and \(1 + r_f\):

\[
1 + r_d = 1 + 0.0422 = 1.0422
\]
\[
1 + r_f = 1 + 0.0258 = 1.0258
\]

Now calculating the ratio:

\[
\frac{(1 + r_d)}{(1 + r_f)} = \frac{1.0422}{1.0258} \approx 1.0159
\]

Now, plug this back into the equation for \(S\):

\[
S = \frac{12.223}{1.0159} \approx 12.03
\]

Thus, the estimated spot exchange rate \(S\) is approximately MXN 12.031 per $.

Therefore, the correct answer is:

**MXN 12.031 per $**