Find the payment made by the ordinary annuity with the given present value
$248,671, quarterly payments for 23 years, interest rate is 7%, compounded quarterly

To find the payment made by an ordinary annuity, we use the Present Value of an Ordinary Annuity (PVOA) formula:

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

Where:
- $ PV $ = Present Value = \$248,671
- $ P $ = Payment (what we need to find)
- $ r $ = interest rate per period = 7% annual interest, compounded quarterly, so $ r = \dfrac{0.07}{4} = 0.0175 $
- $ n $ = total number of payments = $ 23 \, \text{years} \times 4 \, \text{quarters per year} = 92 $

Now, we solve for $ P $ (the payment):

\[
248,671 = \dfrac{P \cdot \left(1 - (1 + 0.0175)^{-92}\right)}{0.0175}
\]

Let's calculate $ P $.The quarterly payment for the ordinary annuity is approximately \$5,458.03.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How does the formula for the future value of an ordinary annuity differ from the present value formula?
2. How would the payments change if the interest rate were compounded monthly instead of quarterly?
3. What would be the total amount paid over the 23 years in this annuity?
4. How does changing the length of the annuity affect the payment amount?
5. What happens to the payment amount if the present value of the annuity increases?

**Tip:** For any financial calculation, ensure you match the compounding period with the payment frequency to avoid miscalculations.

Find the payment made by the ordinary annuity with the given present value $248,671, quarterly payments for 23 years, interest rate is 7%, compounded quarterly.

Learn how to find the payment for an ordinary annuity with a present value of $248,671, quarterly payments for 23 years, and an interest rate of 7% compounded quarterly. This step-by-step solution walks through the PVOA formula, interest rate per period, and total number of payments.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation