To save for​ retirement, a student invests ​$20 each month in an ordinary annuity with 3 % interest compounded monthly. Determine the accumulated amount in the​ student's annuity after 15 years

To solve this problem, we will use the formula for the future value of an ordinary annuity with regular payments and compound interest:

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

Where:
- $A$ is the accumulated amount (future value),
- $P$ is the regular payment amount,
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of payments (years $\times$ 12).

### Given:
- $P = 20$ dollars,
- Annual interest rate = 3%, so monthly interest rate $r = \frac{3\%}{12} = 0.0025$,
- Number of years = 15, so total number of payments $n = 15 \times 12 = 180$.

Now, we can plug these values into the formula to find the accumulated amount $A$.

\[
A = 20 \times \frac{(1 + 0.0025)^{180} - 1}{0.0025}
\]

Let me calculate this for you.The accumulated amount in the student's annuity after 15 years will be approximately **$4,539.45**.

Do you need further clarification or details? Here are five related questions to consider:

1. How would the accumulated amount change if the interest rate increased to 5%?
2. What would happen if the student invested $50 instead of $20 each month?
3. How does the accumulated amount differ between ordinary annuities and annuities due?
4. How does compounding frequency (monthly vs. annually) affect the future value?
5. What would be the effect of adding more years to the investment period?

**Tip:** Small changes in the interest rate can have a significant impact on long-term investments due to compounding.

To save for retirement, a student invests $20 each month in an ordinary annuity with 3% interest compounded monthly. Determine the accumulated amount in the student's annuity after 15 years.

Learn how to calculate the future value of an ordinary annuity where $20 is invested each month at 3% interest compounded monthly for 15 years. Discover how compounding affects long-term investments using key concepts in finance and annuities.

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