Find the present value of the following ordinary annuity.

Periodic Payment

Payment Interval

Term

Interest Rate

Conversion Period

​$2200

1 month

9 years

10​%

annually

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Part 1

The present value is ​$
  
enter your response here. 

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

To find the present value of an ordinary annuity, we'll use the present value of an annuity formula:

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

### Given:
- Periodic payment $R = 2200$ dollars
- Payment interval: 1 month
- Term: 9 years
- Interest rate: 10% per annum
- Compounding period: annually

### Step 1: Determine the number of periods
Since the payments are monthly and the term is 9 years:
\[
n = 9 \times 12 = 108 \text{ periods}
\]

### Step 2: Determine the monthly interest rate
Given that the interest rate is compounded annually, we need to calculate the effective monthly interest rate:

\[
i = \left(1 + \frac{0.10}{1}\right)^{\frac{1}{12}} - 1
\]

### Step 3: Use the present value of an annuity formula
We will now substitute the values into the formula to find the present value $PV$.

Let's calculate this step-by-step.The present value of the ordinary annuity is approximately **$158,886.75**.

Would you like more details on how this was calculated or have any questions?

Here are 8 related questions:
1. How does the compounding period affect the present value of an annuity?
2. What would be the present value if the interest rate were compounded monthly instead of annually?
3. How do you calculate the future value of an annuity?
4. How does the term length affect the present value of the annuity?
5. What is the difference between an ordinary annuity and an annuity due?
6. How would an increase in the interest rate affect the present value?
7. Can you calculate the present value of an annuity with variable payments?
8. What role does the frequency of payments play in the valuation of annuities?

**Tip:** When calculating the present value of annuities, always ensure the interest rate and payment periods are aligned.

Learn how to calculate the present value of an ordinary annuity with $2200 payments, over a 9-year term, at a 10% annual interest rate. Use our step-by-step solution with the present value of an ordinary annuity formula. Round all values to six decimal places as needed.

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