Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$450/month for 19 years at 8%/year compounded monthly

To find the future value (amount) of an ordinary annuity, we use the formula:

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

Where:
- $ A $ is the future value (the amount of the annuity),
- $ P $ is the payment per period ($450),
- $ r $ is the interest rate per period (monthly interest rate),
- $ n $ is the total number of payments.

### Given Data:
- Payment per month, $ P = 450 $ dollars,
- Annual interest rate, $ r_{annual} = 8\% $ per year, so monthly interest rate $ r = \frac{8\%}{12} = \frac{0.08}{12} = 0.006667 $,
- Time period, $ t = 19 $ years, so the number of months $ n = 19 \times 12 = 228 $ months.

Now, I'll calculate the future value using these values.The future value of the ordinary annuity is approximately **$239,572.33**.

Would you like more details or further clarification on how this was calculated?

Here are five related questions for further exploration:
1. What is the future value of the annuity if the interest rate were 6% instead of 8%?
2. How would the future value change if the annuity was compounded quarterly instead of monthly?
3. What would be the present value of this annuity if we wanted to find out how much to invest initially?
4. What happens to the future value if the monthly payment is increased to $500?
5. How would the future value differ for a 25-year term instead of 19 years?

**Tip:** Small changes in interest rates or the number of compounding periods can significantly impact the future value of an annuity!

Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) $450/month for 19 years at 8%/year compounded monthly.

Discover how to calculate the future value of an ordinary annuity with $450 monthly payments for 19 years at an 8% annual interest rate, compounded monthly. This detailed solution uses the future value of an annuity formula, making it ideal for high school and college-level students.

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