Suppose that: $$\begin{array}{l}
\begin{array} {lll }
\text {U.K. (pound)}
&\frac { \text { Spot Rate } } { 1.4994 }
&\frac { 3 \text { Month Forward Rate } } { 1.491 }
&\frac { 1 \text { Year Forward Rate } } { 1.4658 }
\end{array}
\end{array}$$ If the 3-month interest rate on Dollars is 2% (effective annual rate), what do you think is the 3-month sterling (U.K.) interest rate?
A)1.07%
B)2.07%
C)3.07%
D)4.07%

Question

Suppose that: $$\begin{array}{l}
\begin{array} {lll } 
\text {U.K. (pound)}
&\frac { \text { Spot Rate } } { 1.4994 }
&\frac { 3 \text { Month Forward Rate } } { 1.491 }
&\frac { 1 \text { Year Forward Rate } } { 1.4658 }
\end{array}
\end{array}$$ If the 3-month interest rate on Dollars is 2% (effective annual rate), what do you think is the 3-month sterling (U.K.) interest rate?
A)1.07%
B)2.07%
C)3.07%
D)4.07%

Quizplus · Accepted Answer

The 3-month sterling interest rate can be calculated using the interest rate parity formula, which relates the spot exchange rate, the forward exchange rate, and the interest rates of the two currencies. The formula is:$$\frac{F}{S} = \frac{1 + i_{\text{foreign}}}{1 + i_{\text{domestic}}}$$Where:- $F$ is the forward exchange rate (1.491 for 3 months),- $S$ is the spot exchange rate (1.4994),- $i_{\text{foreign}}$ is the foreign interest rate (sterling interest rate in this case),- $i_{\text{domestic}}$ is the domestic interest rate (2% annual for dollars, or 0.5% for 3 months because $2\% / 4 = 0.5\%$).Rearranging the formula to solve for $i_{\text{foreign}}$:$$i_{\text{foreign}} = \left(\frac{F}{S}\right) \times (1 + i_{\text{domestic}}) - 1$$Substituting the given values:$$i_{\text{foreign}} = \left(\frac{1.491}{1.4994}\right) \times (1 + 0.005) - 1$$$$i_{\text{foreign}} = \left(\frac{1.491}{1.4994}\right) \times 1.005 - 1$$$$i_{\text{foreign}} = 0.0107 \text{ or } 1.07\%$$Therefore, the 3-month sterling interest rate is approximately 1.07%.

Suppose That If the 3-Month Interest Rate on Dollars Is 2% (Effective