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To determine the amount of money that must be invested to reach $1,000,000 in 32 years with a 7% annual interest rate, compounded annually, we use the Present Value formula for compound interest:

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

where:
- $FV = 1,000,000$ (the future value, or the target amount),
- $r = 0.07$ (the annual interest rate),
- $n = 32$ years.

Substituting the values:

\[
PV = \frac{1,000,000}{(1 + 0.07)^{32}}
\]

Calculating:

1. $1 + 0.07 = 1.07$
2. $1.07^{32} \approx 8.718$
3. $PV = \frac{1,000,000}{8.718} \approx 114,674$

So, you would need to invest **$114,674** (to the nearest dollar) to become a millionaire in 32 years at a 7% annual interest rate, compounded annually.

Would you like more details or have questions?

Here are some related questions:
1. What is the impact of a different interest rate on the present value required?
2. How would changing the investment period affect the required initial investment?
3. What if compounding were done semi-annually instead of annually?
4. How can inflation affect the future purchasing power of a million dollars?
5. What would the future value be if the initial investment were doubled?

**Tip:** Compound interest grows faster with more frequent compounding periods (e.g., monthly vs. annually).

Determine the amount of money, to the nearest dollar, you must invest at 7% per year, compounded annually, so that you will be a millionaire in 32 years.

Learn how to determine the present value required to reach a million dollars in 32 years with a 7% annual interest rate, compounded annually. This problem covers compound interest concepts and calculations suitable for Grades 11-12.

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