Determine the amount of the ordinary annuity at the end of the given period. (Round your final answer to two decimal places. $100 deposited per month at 1.5% per month for 15 months



To determine the amount of an ordinary annuity, we 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 payment amount per period.
- $ r $ is the interest rate per period.
- $ n $ is the number of periods.

Given:
- $ P = \$100 $
- $ r = 0.015 $ (1.5% per month)
- $ n = 15 $ months

Plugging in the values:

\[ FV = 100 \times \frac{(1 + 0.015)^{15} - 1}{0.015} \]

Let's calculate it step by step:

1. Calculate $ 1 + r $:

\[ 1 + 0.015 = 1.015 \]

2. Raise $ 1.015 $ to the power of 15:

\[ 1.015^{15} \approx 1.2467 \]

3. Subtract 1 from the result:

\[ 1.2467 - 1 = 0.2467 \]

4. Divide by $ r $:

\[ \frac{0.2467}{0.015} \approx 16.4467 \]

5. Multiply by $ P $:

\[ 100 \times 16.4467 \approx 1644.67 \]

Therefore, the amount of the ordinary annuity at the end of 15 months is approximately $ \$1644.67 $.

Would you like more details on this calculation or have any questions?

Here are 8 related questions to expand your understanding:
1. What is the formula for the present value of an ordinary annuity?
2. How would the calculation change if the payments were made at the beginning of each period (annuity due)?
3. What is the effect of a higher interest rate on the future value of an annuity?
4. How would the future value change if the number of periods increased to 20 months?
5. What is the impact of increasing the monthly deposit to $150?
6. How can the future value of an annuity be used in retirement planning?
7. What are some real-life examples of ordinary annuities?
8. How do you calculate the future value of an annuity with varying payments?

**Tip:** When calculating annuities, ensure that the interest rate and the number of periods match the frequency of the payments (e.g., monthly payments with a monthly interest rate).

Learn how to calculate the future value of an ordinary annuity with $100 deposited per month at 1.5% interest over 15 months. Step-by-step solution provided, rounding to two decimal places. Suitable for undergraduate students and anyone interested in financial mathematics.

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