The future value (FV) of an annuity can be calculated using the future value formula for a series of equal payments (PMT):

$FV = PMT \times \frac{(1 + i)^n - 1}{i}$

Where:

• $PMT$ is the payment amount per period,
• $i$ is the interest rate per period,
• $n$ is the number of periods.

Given values:

• $PMT = 98$ dollars,
• $i = 0.03$,
• $n = 41$.

Part 1: Substitute the values into the formula

The correct choice is:

B. $FV = 98 \times \frac{(1 + 0.03)^{41} - 1}{0.03}$

Part 2: Calculate the Future Value

Let's calculate this value.The future value (FV) is approximately $7,709.00.

Summary:

• Substitution into Formula: $FV = 98 \times \frac{(1 + 0.03)^{41} - 1}{0.03}$
• Future Value: $7,709.00

Would you like more details or have any questions?

Follow-up Questions:

1. How does increasing the number of periods (n) affect the future value?
2. What would the future value be if the interest rate was 5% instead of 3%?
3. How would the future value change if the payments were $120 instead of $98?
4. What is the effect of compounding frequency on future value?
5. How does delaying the first payment by one period affect the future value?
6. Can you calculate the present value of this future sum?
7. How does inflation impact the real value of the future sum?
8. What if you want to reach a specific future value, how should you adjust the payment amount?

Tip:

Regular contributions to an investment account, even in small amounts, can grow significantly over time due to the power of compound interest.