Using an annual effective rate of 5.5%, calculate the present value of an annuity that pays 100 at the end of each month for 20 years.

(Round your answer to the nearest two decimal places)

To calculate the present value (PV) of an annuity, we use the following formula for an ordinary annuity:

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

Where:
- \( P \) is the payment per period (100 in this case),
- \( i \) is the interest rate per period,
- \( n \) is the total number of periods.

Given:
- Annual effective rate = 5.5% (or 0.055 as a decimal),
- Monthly payments of 100,
- Duration is 20 years.

### Step 1: Calculate the monthly interest rate
We need to convert the annual effective rate to a monthly rate. The formula to convert the annual effective rate to a monthly rate is:

\[
i = (1 + \text{annual rate})^{\frac{1}{12}} - 1
\]

\[
i = (1 + 0.055)^{\frac{1}{12}} - 1
\]

### Step 2: Calculate the number of periods
Since the payments are monthly and the duration is 20 years:

\[
n = 20 \times 12 = 240
\]

### Step 3: Compute the present value
Now, we will compute the present value using the values for \( i \) and \( n \).

Let me calculate that for you.The present value of the annuity is approximately **14,698.46**.

Would you like more details on the calculation process or any other clarification?

Here are some related questions:
1. How does the annual effective rate affect the present value of an annuity?
2. What would happen if the payment frequency was changed to quarterly?
3. How would an increase in the interest rate impact the annuity's present value?
4. What is the difference between an ordinary annuity and an annuity due?
5. How can we calculate the future value of the same annuity?

**Tip:** When dealing with interest rates, always make sure to convert them appropriately for the period of payments (e.g., monthly, quarterly).

Using an annual effective rate of 5.5%, calculate the present value of an annuity that pays 100 at the end of each month for 20 years. (Round your answer to the nearest two decimal places)

Learn how to calculate the present value of an annuity that pays 100 at the end of each month for 20 years using a 5.5% annual effective interest rate. This problem involves key concepts like the time value of money, annuity formulas, and interest rate conversions. Detailed steps included for finance and mathematics students.

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