# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5 - Page 537: 30

(a) The amount saved after 10 years is $\$956,793$(b) The interest is$\$356,793$

#### 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 $A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$ $A = \frac{(\$15,000)~[(1+\frac{0.09}{4})^{(4)(10)}~-1]}{\frac{0.09}{4}}A = \$956,793$ The amount saved after 10 years is $\$956,793$(b) The total amount of money deposited into the annuity is$\$15,000 \times 40$, which is $\$600,000$The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.$interest = \$956,793 - \$600,000 = \$356,793$ The interest is $\$356,793\$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.