Points] DETAILS MY NOTES, WANEFMAC8 3.2.034. Petermine 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 yee 51,907 SUBMIT ANSWER

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To find the amount of money that needs to be invested now at an annual interest rate of 8% compounded annually to become a millionaire in 38 years, we can use the formula for compound interest:

$$ A = P \left(1 + \frac{r}{100}\right)^n $$

where:
- $$ A $$ is the amount of money after $$ n $$ years,
- $$ P $$ is the principal amount (the amount of money invested now),
- $$ r $$ is the annual interest rate (in %),
- $$ n $$ is the number of years.

Given:
- $$ r = 8\% $$,
- $$ n = 38 $$ years.

We want to find $$ P $$ such that $$ A = 1,000,000 $$ (to become a millionaire).

Substitute the given values into the formula:

$$ 1,000,000 = P \left(1 + \frac{8}{100}\right)^{38} $$

Now, we can solve for $$ P $$ to find the amount of money that needs to be invested now.
Solve the equation by following steps:
- step0: Solve for $$P$$:
  $$1000000=P\left(1+\frac{8}{100}\right)^{38}$$
- step1: Simplify:
  $$1000000=\frac{27^{38}}{25^{38}}\times P$$
- step2: Swap the sides:
  $$\frac{27^{38}}{25^{38}}\times P=1000000$$
- step3: Rewrite the expression:
  $$\frac{27^{38}P}{25^{38}}=1000000$$
- step4: Cross multiply:
  $$27^{38}P=25^{38}\times 1000000$$
- step5: Simplify the equation:
  $$27^{38}P=1000000\times 25^{38}$$
- step6: Divide both sides:
  $$\frac{27^{38}P}{27^{38}}=\frac{1000000\times 25^{38}}{27^{38}}$$
- step7: Divide the numbers:
  $$P=\frac{1000000\times 25^{38}}{27^{38}}$$
The amount of money that needs to be invested now at an annual interest rate of 8% compounded annually to become a millionaire in 38 years is:

$$ P = \frac{1000000 \times 25^{38}}{27^{38}} $$

To find the approximate value of $$ P $$ to the nearest dollar, we can calculate it.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1000000\times 25^{38}}{27^{38}}$$
The amount of money that needs to be invested now at an annual interest rate of 8% compounded annually to become a millionaire in 38 years is approximately $53,690.48 to the nearest dollar.
You need to invest approximately $53,690 now at an 8% annual interest rate, compounded annually, to become a millionaire in 38 years.

Points] DETAILS MY NOTES, WANEFMAC8 3.2.034. Petermine 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 yee 51,907 SUBMIT ANSWER

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