select the correct answer.\nsiobhan will receive a $5,000 lump - sum bonus from work in five years. if she…

Explanation:

Step1: Identify compound - interest formula for present value

The formula for present value $PV$ when compounded $n$ times a year is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $FV$ is the future value, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $FV = 5000$, $r=0.05$ (since $5%=0.05$), $n = 4$ (compounded quarterly), and $t = 5$.

Step3: Substitute values into the formula

$PV=\frac{5000}{(1+\frac{0.05}{4})^{4\times5}}=\frac{5000}{(1 + 0.0125)^{20}}$. First, calculate $(1 + 0.0125)^{20}$. Using a calculator, $(1.0125)^{20}\approx1.282037$. Then, $PV=\frac{5000}{1.282037}\approx3900$.

Answer:

B. $3,900