chapter 5 quiz\nscore: 4/20 answered: 1/5\nquestion 4\nhow much would you need to deposit in an account in…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula for present value is $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, where $A$ is the future value, $P$ is the present value (the amount we need to find), $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert given values to appropriate form

We have $A = 2000$, $r=0.08$ (since $8%=0.08$), $n = 4$ (compounded quarterly), and $t = 15$.

Step3: Substitute values into the formula

$P=\frac{2000}{(1 +\frac{0.08}{4})^{4\times15}}$. First, calculate the value inside the parentheses: $\frac{0.08}{4}=0.02$, and $1+\frac{0.08}{4}=1.02$. Also, $4\times15 = 60$. So we have $P=\frac{2000}{(1.02)^{60}}$.

Step4: Calculate $(1.02)^{60}$

Using a calculator, $(1.02)^{60}\approx3.28103$.

Step5: Calculate $P$

$P=\frac{2000}{3.28103}\approx609.56$.

Answer:

$609.56$