## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5 - Page 536: 18

(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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