To find the future value of an investment $P$ with an annual interest rate $r$ over a time period $t$ when interest is compounded in different ways, we use the following formulas:

(a) Compounded Annually

The formula for future value when interest is compounded annually is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ where:

• $P$ is the principal amount ($1500),
• $r$ is the annual interest rate (3.15% or 0.0315 as a decimal),
• $n$ is the number of times interest is compounded per year (annually, $n = 1$),
• $t$ is the time in years (5 years).

Substituting the given values: $A = 1500 \left(1 + \frac{0.0315}{1}\right)^{1 \times 5}$ $A = 1500 \left(1 + 0.0315\right)^5$ $A = 1500 \left(1.0315\right)^5$ $A \approx 1500 \times 1.168811$ $A \approx 1753.22$

So, the future value of the investment when compounded annually is approximately $1753.22.

Would you like details or have any questions? Here are some related questions to expand on the topic:

1. How does the future value change if the interest rate increases?
2. What is the formula for continuous compounding, and why is it different?
3. How does the compounding frequency affect the future value of an investment?
4. What is the future value when compounded monthly?
5. What is the future value when compounded daily?
6. How is the doubling time $T$ calculated for a given interest rate?
7. What is the impact of extending the investment period to 10 years?
8. How does decreasing the principal amount affect the future value?

Tip: Always round your final answers to the nearest cent when dealing with currency to maintain accuracy in financial calculations.