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: 41

Answer

The value of the account after 16 years will be $\$9187$

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 after 10 years when we invest at a rate of 7% compounded semiannually. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$3000)~(1+\frac{0.07}{2})^{(2)(10)}$ $A = \$5969.37$ After 10 years, there will be $\$5969.37$ in the account. We can find the total amount in the account after 6 more years when we invest at a rate of 7.25% compounded quarterly. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$5969.37)~(1+\frac{0.0725}{4})^{(4)(6)}$ $A = \$9187$ After 6 more years, there will be $\$9187$ in the account. The value of the account after 16 years will be $\$9187$
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