# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 33

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.$A_1-A_2 = \$2,326,274.26-\$257,142.95A_1-A_2 = \$2,069,131$ The first investment would earn \\$2,069,131 more than the second investment.

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