Find the present value of an ordinary annuity of 60 payments of $5200 each made quarterly and earning interest at 2.5%/year compounded quarterly. (Round your answer to the nearest cent.)

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

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

Where:
- $ PV $ = Present Value of the annuity
- $ P $ = Payment per period ($5200)
- $ i $ = Interest rate per period
- $ n $ = Total number of payments

### Given dataTo calculate the present value of an ordinary annuity, we use the formula:

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

Where:
- $ PV $ = Present Value of the annuity
- $ P $ = Payment per period ($5200)
- $ i $ = Interest rate per period
- $ n $ = Total number of payments

### Given 
- Payment $ P = 5200 $
- Annual interest rate = 2.5% per year
- Compounded quarterly → quarterly interest rate $ i = \frac{2.5\%}{4} = \frac{0.025}{4} = 0.00625 $
- Number of payments = 60 (since payments are quarterly, they span 15 years or 60 quarters)

Now, we can substitute the values into the formula:

\[
PV = 5200 \times \left( 1 - (1 + 0.00625)^{-60} \right) / 0.00625
\]

Let me calculate that for you.The present value of the ordinary annuity is approximately \$259,507.60.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How does changing the interest rate affect the present value of the annuity?
2. What is the future value of this annuity after 60 payments?
3. How does the frequency of compounding influence the annuity value?
4. What if the payments were made monthly instead of quarterly?
5. How would the present value change if the number of payments increased to 80?

**Tip:** The more frequent the compounding periods, the greater the effect of interest on both the present and future value of annuities.

Find the present value of an ordinary annuity with 60 quarterly payments of $5200 and an interest rate of 2.5% compounded quarterly. This solution demonstrates the present value annuity formula, key algebraic concepts, and the impact of compounding over time. Suitable for advanced high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation