We Pay Insurance Company will pay you $1,125 each quarter for 25 years. You want to earn a minimum interest rate of .86 percent per quarter. What is the most you are willing to pay today for these payments?

Multiple Choice

$72,746.05

$177,185.86

$75,254.54

$71,491.81

$74,776.72

This is a **present value of an annuity** problem, where you are receiving fixed payments over a period of time and want to determine how much these future payments are worth today based on a specific interest rate.

The formula for the present value of an annuity is:

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

Where:
- $PV$ is the present value (the amount you're willing to pay today)
- $P$ is the quarterly payment ($1,125)
- $r$ is the interest rate per quarter (0.86% = 0.0086)
- $n$ is the total number of payments (25 years × 4 quarters = 100)

Now let's calculate the present value.

I'll work out the solution.The present value of the annuity is approximately **$75,254.54**.

Thus, the most you should be willing to pay today is **$75,254.54**, which matches the third option.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the present value change if the interest rate was 1% per quarter?
2. What if the quarterly payments were $2,000 instead of $1,125?
3. How does increasing the number of periods affect the present value of an annuity?
4. What is the future value of these payments after 25 years at 0.86% interest per quarter?
5. How does compounding frequency affect the overall value of an annuity?

**Tip:** In annuity calculations, a small change in the interest rate can have a significant impact on the present value.

We Pay Insurance Company will pay you $1,125 each quarter for 25 years. You want to earn a minimum interest rate of .86 percent per quarter. What is the most you are willing to pay today for these payments? Multiple Choice: $72,746.05, $177,185.86, $75,254.54, $71,491.81, $74,776.72

Determine how much you should pay today for quarterly payments of $1,125 over 25 years at an interest rate of 0.86% per quarter. Learn how to calculate the present value of an annuity using the correct formula and understand the concept of time value of money. Suitable for advanced high school or college students.

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