(1 point) If you make quarterly payments of $381.00 into an ordinary annuity earning an annual interest rate of 5.48% compounded quarterly, how much will you have in the account after 8

 years?

To calculate how much you will have in the account after 8 years, we need to use the formula for the future value of an ordinary annuity:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the payment made each period (\$381.00).
- $r$ is the interest rate per period.
- $n$ is the total number of periods.

### Step 1: Identify the values

- Quarterly payments, $P = 381.00$
- Annual interest rate = 5.48%, so the quarterly interest rate is $ \frac{5.48\%}{4} = 1.37\% = 0.0137 $ per quarter.
- Number of years = 8, so the number of periods (quarters) is $ 8 \times 4 = 32 $ periods.

### Step 2: Plug into the formula

\[
FV = 381 \times \frac{(1 + 0.0137)^{32} - 1}{0.0137}
\]

Now, let's calculate the future value.The future value of the ordinary annuity after 8 years will be approximately **$15,173.77**.

Would you like more details on how the calculation works, or do you have any other questions?

Here are five related questions you might find interesting:
1. How would the future value change if the interest rate were higher?
2. What happens to the future value if the payment amount increases?
3. How does the number of periods (quarters) affect the future value?
4. How do you calculate the present value of an annuity with the same parameters?
5. How would the future value change if the payments were made at the beginning of each period (annuity due)?

Tip: When dealing with annuities, it's important to remember whether the payments are made at the beginning or the end of each period. This changes the formula slightly.

If you make quarterly payments of $381.00 into an ordinary annuity earning an annual interest rate of 5.48% compounded quarterly, how much will you have in the account after 8 years?

Calculate the future value of an ordinary annuity with quarterly payments of $381.00, an annual interest rate of 5.48%, and 8 years of investment. This step-by-step solution covers key concepts such as compound interest, annuities, and time value of money, suitable for high school students in Grades 10-12.

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