Find the present value of an ordinary annuity of 60 payments of $5300 each made quarterly and earning interest at 3.5%/year compounded quarterly. (Round your answer to the nearest cent.)

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

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

Where:
- $ PV $ is the present value of the annuity,
- $ P $ is the payment amount per period,
- $ r $ is the interest rate per period,
- $ n $ is the total number of payments.

### Given:
- $ P = 5300 $ (the quarterly payment),
- Annual interest rate is 3.5%, compounded quarterly,
- Total number of payments $ n = 60 $ (15 years of quarterly payments),
- Quarterly interest rate $ r = \frac{3.5\%}{4} = \frac{0.035}{4} = 0.00875 $.

Now, we can substitute these values into the formula:

\[
PV = 5300 \times \left( \frac{1 - (1 + 0.00875)^{-60}}{0.00875} \right)
\]

Let's calculate this.The present value of the ordinary annuity is approximately \$246,581.58, rounded to the nearest cent.

Would you like any further details or clarification? 

Here are some related questions you might consider:
1. How does changing the interest rate affect the present value of an annuity?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would the present value change if payments were made monthly instead of quarterly?
4. What happens to the present value if the payment amount increases?
5. How can you calculate the future value of this same annuity?

**Tip:** The present value of an annuity decreases as the interest rate increases.

Calculate the present value of an ordinary annuity with 60 quarterly payments of $5300 and an interest rate of 3.5% compounded quarterly. Learn the key concepts of annuities, present value, and compound interest with a detailed step-by-step solution. Suitable for Grades 11-12 and college-level students.

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