## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 68

The ending balance in the account will be $\$8544.49$#### 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 at the end of 2 years when we invest at a rate of 8% compounded monthly.$A = P~(1+\frac{r}{n})^{nt}A = (\$5000)~(1+\frac{0.08}{12})^{(12)(2)}$ $A = \$5864.44$After 2 years, there will be$\$5864.44$ in the account. Then, $\$1500$is withdrawn, so there will be a total of$\$4364.44$ in the account. We can find the total amount in the account after 1 more year when we invest at a rate of 8% compounded monthly. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$4364.44)~(1+\frac{0.08}{12})^{(12)(1)}A = \$4726.69$ After 1 more year, there will be $\$4726.69$in the account. Then,$\$2000$ is put in the account, so there will be a total of $\$6726.69$in the account. We can find the total amount in the account after 3 more years when we invest at a rate of 8% compounded monthly.$A = P~(1+\frac{r}{n})^{nt}A = (\$6726.69)~(1+\frac{0.08}{12})^{(12)(3)}$ $A = \$8544.49$The ending balance in the account will be$\$8544.49$

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