#### Answer

The first investment would earn \$2,069,131 more than the second investment.

#### Work Step by Step

This is the formula we use when we make calculations with compound interest:
$A = P~(1+\frac{r}{n})^{nt}$
$A$ is the final amount in the account
$P$ is the principal (the amount of money invested)
$r$ is the interest rate
$n$ is the number of times per year the interest is compounded
$t$ is the number of years
We can find the total amount in the account $A_1$ after 40 years when we invest at a rate of 12% for 40 years.
$A = P~(1+\frac{r}{n})^{nt}$
$A_1 = (\$25,000)~(1+\frac{0.12}{1})^{(1)(40)}$
$A_1 = \$2,326,274.26$
After 40 years, there will be \$2,326,274.26 in the account.
We can find the total amount in the account $A_2$ after 40 years when we invest at a rate of 6% for 40 years.
$A = P~(1+\frac{r}{n})^{nt}$
$A_2 = (\$25,000)~(1+\frac{0.06}{1})^{(1)(40)}$
$A_2 = \$257,142.95$
After 40 years, there will be \$257,142.95 in the account.
We can find the difference between the first investment and the second investment.
$A_1-A_2 = \$2,326,274.26-\$257,142.95$
$A_1-A_2 = \$2,069,131$
The first investment would earn \$2,069,131 more than the second investment.