https://file.aiquickdraw.com/mathbot/file/172643260524254vsaenf.jpg

The question asks you to determine how much you need to invest monthly to reach $1.1 million in 23 years, given a 6% annual percentage rate (APR).

This is a future value of annuity problem, and we can use the savings plan formula, also known as the future value of an ordinary annuity formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ FV $ is the future value (the amount you want to have in 23 years, $1,100,000),
- $ P $ is the monthly deposit (the unknown we need to solve for),
- $ r $ is the monthly interest rate (6% APR divided by 12 months = 0.06/12 = 0.005),
- $ n $ is the number of months (23 years × 12 = 276 months).

We can rearrange the formula to solve for $ P $:

\[
P = \frac{FV}{\frac{(1 + r)^n - 1}{r}}
\]

Let me calculate that for you.You should invest approximately **$1857.32** each month to reach $1.1 million in 23 years, assuming an APR of 6%.

Would you like any further details on this calculation or have any other questions?

Here are 5 related questions to consider:
1. How does changing the APR affect the monthly investment needed?
2. What would the monthly investment be if the goal was $2 million instead of $1.1 million?
3. How much total interest will you have earned after 23 years?
4. How would the investment change if you made yearly instead of monthly contributions?
5. What would happen if you started saving at a different age, say 35 instead of 42?

**Tip:** The earlier you start saving, the less you need to invest monthly due to the power of compound interest!

At age 42, you start saving for retirement. If your investment plan pays an APR of 6% and you want to have $1.1 million when you retire in 23 years, how much should you deposit monthly?

Learn how to calculate the monthly deposits needed to save $1.1 million in 23 years with a 6% APR using the future value of annuity formula. Explore key concepts in annuities and compound interest. Perfect for undergraduate students or anyone learning about savings plans.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation