https://file.aiquickdraw.com/mathbot/file/1727584664178a3alln6y.jpg

The problem you're working on asks to calculate the **present value** (PV) of a lump sum investment that will grow to $1,000,000 over 40 years with an APR of 4%, compounded quarterly. 

The **present value formula** for compound interest is:

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

Where:
- $FV = 1,000,000$ is the future value.
- $r = 0.04$ is the annual interest rate (4% as a decimal).
- $n = 4$ because the interest is compounded quarterly (4 times a year).
- $t = 40$ is the number of years.
  
Now, let's calculate the present value.The amount you need to invest now as a lump sum to have $1,000,000 after 40 years, with an APR of 4% compounded quarterly, is approximately **$203,507.39**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the present value change if the APR were 5% instead of 4%?
2. What would happen to the present value if the investment were compounded monthly instead of quarterly?
3. How does the present value formula relate to the future value formula?
4. What impact would investing for 50 years instead of 40 years have on the required present value?
5. How does changing the compounding frequency affect the total interest earned?

**Tip:** The more frequently interest is compounded, the greater the impact on the total return due to compounding effects.

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $1,000,000 after 40 years with an APR of 4% compounded quarterly. Round your answer to the nearest cent, if necessary.

Learn how to calculate the present value needed to invest as a lump sum to reach $1,000,000 in 40 years, with a 4% APR compounded quarterly. This guide covers compound interest, the present value formula, and exponential growth concepts, suitable for 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