What is the future value of an annuity with the following information:

12 years
8% compounded monthly
A monthly deposit of $500
A current balance of $0.
Rounded to the nearest $.
Question 5Answer

$73,298


$120,254


$6,225


$100,298

To find the future value of an annuity with regular monthly deposits, we can use the Future Value of an Ordinary Annuity formula:

\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]

Where:
- $FV$ is the future value of the annuity.
- $P$ is the regular deposit (monthly).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of deposits (months).

Given:
- Monthly deposit $P = 500$,
- Annual interest rate $i = 8\% = 0.08$,
- Time = 12 years,
- Compounding is monthly, so the interest rate per month $r = \frac{0.08}{12} = 0.0066667$,
- Number of months $n = 12 \times 12 = 144$.

Let's calculate the future value $FV$.The future value of the annuity, with the given parameters, is approximately **$120,254**, which matches one of the provided answer choices.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the future value change with a higher interest rate?
2. What if the deposits were made at the beginning of the month instead of the end?
3. How would a shorter duration (e.g., 10 years) affect the future value?
4. How does compounding frequency impact the future value of an annuity?
5. What would happen if the monthly deposit increased to $600?

**Tip:** Increasing the frequency of compounding generally leads to a higher future value, as interest accumulates more often.

What is the future value of an annuity with the following information: 12 years, 8% compounded monthly, a monthly deposit of $500, a current balance of $0. Rounded to the nearest $.

Find the future value of an annuity with monthly deposits of $500 over 12 years at 8% interest compounded monthly. This step-by-step guide explains the use of the future value of an ordinary annuity formula, key concepts of compound interest, and how time affects the growth of savings.

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