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: 14

Answer

(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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