Determine the rate of return for the following investments. 
 
a. A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually. 

To determine the rate of return for this investment, we need to calculate the **future value (FV)** of the Guaranteed Investment Certificate (GIC) and then find the rate of return.

We will use the **compound interest formula**:

\[
FV = PV \times \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ FV $ is the future value of the investment.
- $ PV $ is the present value (initial investment), which is \$40,000.
- $ r $ is the annual interest rate (6.5% or 0.065).
- $ n $ is the number of times the interest is compounded per year (since it's compounded annually, $ n = 1 $).
- $ t $ is the time in years (5 years).

### Step 1: Apply the values to the formula

\[
FV = 40,000 \times \left(1 + \frac{0.065}{1}\right)^{1 \times 5}
\]
\[
FV = 40,000 \times \left(1.065\right)^5
\]

### Step 2: Calculate the future value

\[
FV = 40,000 \times 1.37009 = 54,803.72
\]

So, the future value of the investment is approximately **\$54,803.72**.

### Step 3: Calculate the total return

The total return is the difference between the future value and the initial investment:

\[
\text{Total Return} = 54,803.72 - 40,000 = 14,803.72
\]

### Step 4: Calculate the rate of return

The rate of return can be found as:

\[
\text{Rate of Return} = \frac{\text{Total Return}}{\text{Initial Investment}} \times 100
\]

\[
\text{Rate of Return} = \frac{14,803.72}{40,000} \times 100 \approx 37.01\%
\]

Thus, the rate of return over the 5-year period is approximately **37.01%**.

---

Would you like further details or explanations on any of the steps? Here are five related questions you might explore:

1. How would the rate of return change if the interest were compounded quarterly instead of annually?
2. What is the effective annual rate (EAR) for this investment?
3. How does compound interest compare with simple interest over a 5-year period at the same rate?
4. What would the future value be if the interest rate was reduced to 5%?
5. How does inflation affect the real value of the return?

**Tip:** Always check how frequently interest is compounded, as it significantly affects the total return on an investment.

Determine the rate of return for the following investments. a. A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually.

Learn how to calculate the rate of return for a 5-year $40,000 GIC with a 6.5% interest rate compounded annually. This detailed solution covers the compound interest formula, rate of return calculations, and step-by-step guidance for financial mathematics. Suitable for high school students in Grades 9-12.

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