## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5: 14

(a) The periodic deposit is $\$1405$(b) The total amount of money deposited into the annuity is$\$168,600$ The interest is $\$81,400$#### 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$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}P = \frac{(\$250,000)~(\frac{0.075}{12})}{~(1+\frac{0.075}{12})^{(12)(10)}~-1}$ $P = \$1405$The periodic deposit is$\$1405$ (b) The total amount of money deposited into the annuity is $\$1405 \times 120$, which is$\$168,600$ The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest. $interest = \$250,000 - \$168,600 = \$81,400$The interest is$\$81,400$

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