## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5: 2

#### Answer

(a) The value of the annuity is $\$89,334$(b) The interest is$\$29,334$

#### 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 $A = \frac{P~[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$ $A = \frac{(\$3000)~[(1+\frac{0.04}{1})^{(1)(20)}-1]}{\frac{0.04}{1}}A = \$89,334$ The value of the annuity is $\$89,334$(b) The total amount of money deposited into the annuity is$\$3000 \times 20$ which is $\$60,000$The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.$interest = \$89,334 - \$60,000 = \$29,334$ The interest is $\$29,334\$

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