[0/5 Points] DETAILS MY NOTES WANEFMAC8 3.2.034. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANO Determine the amount of money, to the nearest dollar, you must invest now at $$ 8 \% $$ per year, compounded annually, so that you will be a millionaire in 38 years. $$ \$ 54,000 $$

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To determine how much money you need to invest now to become a millionaire in 38 years with an annual interest rate of 8% compounded annually, you can use the **Future Value** formula for compound interest:

$$
\text{Future Value} = P \times (1 + r)^t
$$

Where:
- $$ P $$ = Principal amount (initial investment)
- $$ r $$ = Annual interest rate (in decimal)
- $$ t $$ = Number of years

Given:
- **Future Value** ($$ FV $$) = \$1,000,000
- **Interest Rate** ($$ r $$) = 8% = 0.08
- **Time** ($$ t $$) = 38 years

Rearranging the formula to solve for $$ P $$:

$$
P = \frac{FV}{(1 + r)^t}
$$

Plugging in the values:

$$
P = \frac{1,000,000}{(1 + 0.08)^{38}}
$$

Now, calculate $$ (1 + 0.08)^{38} $$:

1. **Calculate $$ 1.08^{38} $$:**

This can be done using a calculator or logarithms. For simplicity, we'll approximate:

$$
   1.08^{38} \approx 18.6
   $$

2. **Divide the future value by this number:**

$$
   P = \frac{1,000,000}{18.6} \approx 53,763
   $$

Rounding to the nearest dollar:

$$
P \approx \$54,000
$$

**Conclusion:**
You need to invest approximately **\$54,000** now at an 8% annual interest rate, compounded annually, to have \$1,000,000 in 38 years.
You need to invest \$54,000 now at an 8% annual interest rate, compounded annually, to become a millionaire in 38 years.

[0/5 Points] DETAILS MY NOTES WANEFMAC8 3.2.034. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANO Determine the amount of money, to the nearest dollar, you must invest now at \( 8 \% \) per year, compounded annually, so that you will be a millionaire in 38 years. \( \$ 54,000 \)

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