Use the future value formula to find the indicated value.

n equals 41n=41​; 

i equals 0.03i=0.03​; 

PMT equals $ 98PMT=$98​; 

FV equals question markFV=?

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Part 1

Substitute the values into the future value formula. Choose the correct answer​ below, and fill in the answer boxes to complete your choice.

A.

FVequals=nothing left parenthesis 1 plus nothing right parenthesis Superscript nothingenter your response here1+enter your response hereenter your response here

B.

FVequals=98 times StartFraction left parenthesis 1 plus 0.03 right parenthesis Superscript 41 Baseline minus 1 Over 0.03 EndFraction9898•1+0.030.034141−10.030.03

Your answer is correct.

C.

FVequals=nothing left parenthesis 1 minus nothing right parenthesis Superscript nothingenter your response here1−enter your response hereenter your response here

D.

FVequals=nothing times StartFraction left parenthesis 1 minus nothing right parenthesis Superscript nothing Baseline plus 1 Over nothing EndFractionenter your response here•1−enter your response hereenter your response here+1enter your response here

Part 2

FVequals=​$enter your response here

​(Round to the nearest​ cent.)

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.

Learn how to use the future value formula to calculate the future value of an annuity. This problem involves substituting given values into the formula and calculating the future value for a series of equal payments over a specified period. Suitable for high school students learning financial mathematics.

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