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: 16

Answer

The investment yields a greater return over four years when it is invested at 8.25% compounded quarterly.

Work Step by Step

To find the total amount in the account after 4 years when we invest at 8.25% compounded quarterly, we can use this formula: $A = P~(1+\frac{r}{n})^{nt}$ $A$ 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 $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$6,000)~(1+\frac{0.0825}{4})^{(4)(4)}$ $A = \$8317.84$ After 4 years, there will be \$8317.84 in the account. We can find the total amount in the account when we invest at 8.3% compounded semiannually. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$6,000)~(1+\frac{0.083}{2})^{(2)(4)}$ $A = \$8306.64$ After 4 years, there will be \$8306.64 in the account. The investment yields a greater return over four years when it is invested at 8.25% compounded quarterly.
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