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: 67

Answer

The balance in the account after 6 years will be $\$12,942.95$

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 5% compounded semiannually. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$6000)~(1+\frac{0.05}{2})^{(2)(2)}$ $A = \$6622.88$ After 2 years, there will be $\$6622.88$ in the account. Then, an additional $\$4000$ is deposited, so there will be a total of $\$10,622.88$ in the account. We can find the total amount in the account after 4 more years when we invest at a rate of 5% compounded semiannually. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$10,622.88)~(1+\frac{0.05}{2})^{(2)(4)}$ $A = \$12,942.95$ After 4 more years, there will be $\$12,942.95$ in the account. The balance in the account after 6 years will be $\$12,942.95$
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