Find the present value of the ordinary annuity. (Round your answer to the nearest cent.)
Amount of Deposit
m    	Frequency
n    	Rate
r    	Time
t
$500    	annually    	4%    	25 yr

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

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

Where:
- $ PV $ is the present value (what we're solving for),
- $ P $ is the payment amount per period,
- $ r $ is the interest rate per period,
- $ n $ is the number of periods per year,
- $ t $ is the total number of years.

### Given values:
- $ P = 500 $ (the amount of deposit),
- $ r = 4\% = 0.04 $,
- $ t = 25 $ years,
- Since the payments are made annually, $ n = 1 $.

Now, we can substitute the values into the formula:

\[
PV = 500 \times \left( 1 - (1 + 0.04)^{-25} \right) \div 0.04
\]

I'll calculate the present value.The present value of the ordinary annuity is approximately **$7,811.04**.

Would you like any additional details or have further questions?

Here are 5 related questions to expand your understanding:
1. How does 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 changing the deposit amount to $600 affect the present value?
4. How does the frequency of payments (e.g., semiannually) impact the present value calculation?
5. What if the annuity period is extended to 30 years instead of 25?

**Tip:** The higher the interest rate, the lower the present value of an annuity because future payments are discounted more heavily.

Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) Amount of Deposit $500, Frequency annually, Rate 4%, Time 25 years

Learn how to calculate the present value of an ordinary annuity with $500 annual deposits at a 4% interest rate over 25 years. This example demonstrates the time value of money and the annuity present value formula, suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation