Find the present value of the following future amount.
​$300 comma 000 at 11​% compounded annually for 15 years
Question content area bottom
Part 1
What is the present​ value?
​$
  
enter your response here
​(Round to the appropriate​ cent.)

To find the present value $ PV $ of a future amount $ FV $, we use the present value formula for compound interest:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Where:
- $ FV = 300,000 $ (the future value)
- $ r = 11\% = 0.11 $ (the annual interest rate)
- $ t = 15 $ years (the number of years)

Now, let's calculate this step by step.

\[
PV = \frac{300,000}{(1 + 0.11)^{15}}
\]

First, calculate $ (1 + 0.11)^{15} $.

\[
(1.11)^{15} = ?
\]

Now I'll compute the present value.The present value of $ 300,000 $ dollars at 11% compounded annually for 15 years is approximately $ 62,701.30 $ dollars.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How does changing the interest rate affect the present value?
2. What would the present value be if the interest were compounded monthly instead of annually?
3. How does the length of the time period (years) impact the present value?
4. What if the future value was different—say $500,000 instead of $300,000?
5. How would inflation impact the real value of the future amount?

**Tip:** Compounding frequency (annually, monthly, etc.) has a significant impact on the present value. Be sure to note how often compounding occurs in financial problems.

Find the present value of the following future amount. $300,000 at 11% compounded annually for 15 years. What is the present value? (Round to the appropriate cent.)

Learn how to calculate the present value of $300,000 compounded annually at 11% over 15 years. This problem demonstrates the use of the present value formula and highlights key concepts in finance, including compound interest. Suitable for high school seniors and college-level finance courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation