how much would you need to deposit in an account now in order to have $15,000 in the account in 8 years…

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, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to correct form

We have $A = 15000$, $r=0.038$ (since $3.8%=0.038$), $n = 4$ (compounded quarterly), and $t = 8$.

Step3: Substitute values into the formula

$P=\frac{15000}{(1 +\frac{0.038}{4})^{4\times8}}$. First, calculate the value inside the parentheses: $\frac{0.038}{4}=0.0095$, and $1+\frac{0.038}{4}=1.0095$. Then, calculate the exponent: $4\times8 = 32$. So, $(1.0095)^{32}\approx1.34777$. Finally, $P=\frac{15000}{1.34777}\approx11129.49$.

Answer:

$11129.49$