Here's a sample exam question related to forward prices, along with a step-by-step solution.

### **Sample Exam Question:**
A forward contract is written on a stock currently priced at $120. The risk-free interest rate is 6% per annum, compounded continuously. The forward contract matures in 9 months. Assume there are no dividends paid by the stock. 

**Question:**  
Calculate the forward price of the stock.

### **Solution:**

#### **Step 1: Identify the Given Information**
- Spot price of the stock ($S_0$) = $120
- Risk-free interest rate ($r$) = 6% per annum = 0.06 (expressed as a decimal)
- Time to maturity ($T$) = 9 months = 9/12 years = 0.75 years
- No dividends are paid by the stock.

#### **Step 2: Apply the Forward Price Formula**
The formula to calculate the forward price $F$ is:

\[
F = S_0 \times e^{r \times T}
\]

#### **Step 3: Substitute the Values**
Substituting the given values into the formula:

\[
F = 120 \times e^{0.06 \times 0.75}
\]

#### **Step 4: Calculate the Exponential Term**
First, calculate the exponent:

\[
0.06 \times 0.75 = 0.045
\]

Now, calculate $e^{0.045}$:

\[
e^{0.045} \approx 1.04603
\]

#### **Step 5: Calculate the Forward Price**
Now, multiply this value by the spot price:

\[
F = 120 \times 1.04603 \approx 125.52
\]

#### **Final Answer:**
The forward price of the stock is **$125.52**.

Would you like further details or have any questions?

### Related Questions:
1. What would the forward price be if the contract matured in 6 months instead of 9?
2. How does the forward price change if the interest rate decreases to 4%?
3. How would the forward price be affected if the stock paid a dividend during the contract period?
4. What happens to the forward price if the spot price suddenly increases by $10?
5. How would you hedge a position in a forward contract using the underlying asset?

### Tip:
Always make sure to express the time to maturity in years when using the forward price formula, even if the contract period is given in months.

Learn how to calculate the forward price of a stock using the forward price formula with a detailed step-by-step solution. This problem covers finance concepts, including spot price, interest rates, and exponential functions. Suitable for undergraduate students studying finance.

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