Find the payment made by the ordinary annuity with the given present value. $79,925; monthly payments for 27 years; interest rate is 4.1%, compounded monthly

To find the payment made by an ordinary annuity, we use the Present Value of an Ordinary Annuity formula:

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

Where:
- $PV$ is the present value of the annuity (79,925 in this case),
- $P$ is the payment per period (which we are solving for),
- $r$ is the periodic interest rate (annual interest rate divided by number of compounding periods per year),
- $n$ is the total number of payments.

### Given:
- $PV = 79,925$,
- Interest rate is 4.1% compounded monthly, so the periodic rate $r = \frac{4.1\%}{12} = \frac{0.041}{12} = 0.0034167$,
- Number of years = 27, so the total number of payments $n = 27 \times 12 = 324$.

Let's solve for $P$, the monthly payment.

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

I'll calculate it now.The monthly payment for the ordinary annuity is approximately \$408.29.

Would you like more details or have any questions? Here are five related questions to explore further:

1. How would the payment change if the interest rate increased to 5%?
2. What would be the effect on payments if the term was shortened to 20 years?
3. How does compounding frequency affect the overall cost of an annuity?
4. Can you calculate the total amount paid over the entire 27 years?
5. How does an ordinary annuity differ from an annuity due?

**Tip:** Increasing the interest rate or the term length will generally result in higher total payments, even if the monthly payment remains lower.

Find the payment made by the ordinary annuity with the given present value. $79,925; monthly payments for 27 years; interest rate is 4.1%, compounded monthly.

Learn how to calculate the monthly payment for an ordinary annuity with a present value of $79,925, a term of 27 years, and a 4.1% interest rate compounded monthly. This problem covers key concepts such as present value, annuity formulas, and compounding.

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