Thinking Mathematically (6th Edition)

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

Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5: 18

Answer

(a) The periodic deposit is $\$1122$ (b) The total amount of money deposited into the annuity is $\$22,440$ The interest is $\$2560$

Work Step by Step

(a) This is the formula we use to calculate the value of an annuity: $A = \frac{P~[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$ $A$ is the future value of the annuity $P$ is the amount of the periodic deposit $r$ is the interest rate $n$ is the number of times per year the interest is compounded $t$ is the number of years $A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$ $P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$ $P = \frac{(\$25,000)~(\frac{0.045}{4})}{~(1+\frac{0.045}{4})^{(4)(5)}~-1}$ $P = \$1122$ The periodic deposit is $\$1122$ (b) The total amount of money deposited into the annuity is $\$1122 \times 20$, which is $\$22,440$ The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest. $interest = \$25,000 - \$22,440 = \$2560$ The interest is $\$2560$
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