Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

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

Answer

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 Then, $\$1500$ is withdrawn, so there will be a total of $\$4364.44$ in the account.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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