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: 15

Answer

(a) The periodic deposit is $\$355$ (b) The total amount of money deposited into the annuity is $\$170,400$ The interest is $\$829,600$

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 $A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$ $P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$ $P = \frac{(\$1,000,000)~(\frac{0.0725}{12})}{~(1+\frac{0.0725}{12})^{(12)(40)}~-1}$ $P = \$355$ The periodic deposit is $\$355$ (b) The total amount of money deposited into the annuity is $\$355 \times 480$, which is $\$170,400$ The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest. $interest = \$1,000,000 - \$170,400 = \$829,600$ The interest is $\$829,600$
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