# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5: 29

(a) The amount saved after 10 years is $\$693,031$(b) The interest is$\$293,031$

#### 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 $A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$ $A = \frac{(\$10,000)~[(1+\frac{0.105}{4})^{(4)(10)}~-1]}{\frac{0.105}{4}}A = \$693,031$ The amount saved after 10 years is $\$693,031$(b) The total amount of money deposited into the annuity is$\$10,000 \times 40$, which is $\$400,000$The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.$interest = \$693,031 - \$400,000 = \$293,031$ The interest is $\$293,031\$

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