Due to the integrated nature of their capital markets, investors in both the United States and the U.K. require the same real interest rate, 2.5 percent, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3.5 percent in the United States and 1.5 percent in the U.K. for the next three years. The spot exchange rate is currently $1.50 per £.
ROUND ALL ANSWERS 4 DECIMALS

Required:
Compute the nominal interest rate per annum in both the United States and the U.K., assuming that the Fisher effect holds.
What is your expected future spot dollar-pound exchange rate in three years from now?
Can you infer the forward dollar-pound exchange rate for one-year maturity?


### 1. **Compute the Nominal Interest Rate in the U.S. and U.K. (Fisher Effect)**

The Fisher Effect states that the nominal interest rate ($i$) is the sum of the real interest rate ($r$) and the expected inflation rate ($\pi$):

\[
i = r + \pi
\]

Given:
- Real interest rate ($r$) = 2.5% = 0.025
- Inflation rate in the U.S. ($\pi_{US}$) = 3.5% = 0.035
- Inflation rate in the U.K. ($\pi_{UK}$) = 1.5% = 0.015

#### U.S. Nominal Interest Rate ($i_{US}$):

\[
i_{US} = r + \pi_{US} = 0.025 + 0.035 = 0.060 \text{ or } 6.0\%
\]

#### U.K. Nominal Interest Rate ($i_{UK}$):

\[
i_{UK} = r + \pi_{UK} = 0.025 + 0.015 = 0.040 \text{ or } 4.0\%
\]

### 2. **Expected Future Spot Exchange Rate in Three Years**

The future spot exchange rate can be calculated using the concept of purchasing power parity (PPP). The formula for the expected future spot exchange rate is:

\[
E[S_t] = S_0 \times \left( \frac{1 + \pi_{US}}{1 + \pi_{UK}} \right)^t
\]

Where:
- $S_0$ = Current spot exchange rate = $1.50 per £
- $\pi_{US}$ = U.S. inflation rate = 3.5% = 0.035
- $\pi_{UK}$ = U.K. inflation rate = 1.5% = 0.015
- $t$ = Time period = 3 years

\[
E[S_3] = 1.50 \times \left( \frac{1 + 0.035}{1 + 0.015} \right)^3
\]

Let's calculate this.

\[
E[S_3] = 1.50 \times \left( \frac{1.035}{1.015} \right)^3 = 1.50 \times \left( \frac{1.0197}{1.015} \right)^3
\]

\[
E[S_3] \approx 1.50 \times \left(1.0197\right)^3
\]

\[
E[S_3] \approx 1.50 \times 1.0599 = 1.5898
\]

**Expected future spot exchange rate**: $E[S_3] \approx 1.5898$ (rounded to 4 decimal places).

### 3. **Forward Dollar-Pound Exchange Rate for One-Year Maturity**

Using the interest rate parity (IRP) formula:

\[
F_1 = S_0 \times \frac{1 + i_{US}}{1 + i_{UK}}
\]

Where:
- $F_1$ = Forward exchange rate for one-year maturity
- $S_0$ = Current spot exchange rate = $1.50 per £
- $i_{US}$ = U.S. nominal interest rate = 6.0% = 0.060
- $i_{UK}$ = U.K. nominal interest rate = 4.0% = 0.040

\[
F_1 = 1.50 \times \frac{1 + 0.060}{1 + 0.040} = 1.50 \times \frac{1.060}{1.040} = 1.50 \times 1.0192 = 1.5288
\]

**Forward exchange rate**: $F_1 \approx 1.5288$ (rounded to 4 decimal places).

---

### Summary of Results:
1. **U.S. Nominal Interest Rate**: $6.0\%$
2. **U.K. Nominal Interest Rate**: $4.0\%$
3. **Expected Future Spot Exchange Rate in 3 Years**: $1.5898$ $/£
4. **Forward Exchange Rate for 1-Year Maturity**: $1.5288$ $/£

Would you like more details on any of these calculations, or do you have any questions?

### Related Questions:
1. How does the Fisher Effect influence exchange rates in the long term?
2. What are the implications of a higher U.S. inflation rate on international trade?
3. How does purchasing power parity (PPP) relate to the Fisher Effect?
4. What is the difference between nominal and real interest rates?
5. How can forward exchange rates be used for hedging against currency risk?

### Tip:
The Fisher Effect is a key concept in understanding how inflation expectations are embedded into nominal interest rates, and it plays a crucial role in international finance.

Due to the integrated nature of their capital markets, investors in both the United States and the U.K. require the same real interest rate, 2.5 percent, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3.5 percent in the United States and 1.5 percent in the U.K. for the next three years. The spot exchange rate is currently $1.50 per £. ROUND ALL ANSWERS 4 DECIMALS. Compute the nominal interest rate per annum in both the United States and the U.K., assuming that the Fisher effect holds. What is your expected future spot dollar-pound exchange rate in three years from now? Can you infer the forward dollar-pound exchange rate for one-year maturity?

Solve a finance problem involving the Fisher Effect to compute nominal interest rates in the U.S. and U.K. Learn how to calculate the expected future spot exchange rate and the forward exchange rate for one-year maturity. Ideal for finance students.

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