solve the problem. round to the nearest cent. mrs. stevens wants to have $18,000 in the bank in 3 years. if…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ 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. Here, $P = 9500$, $r=0.04$, $n = 4$ (compounded quarterly), and $t = 3$.

Step2: Calculate the future value of the deposit

Substitute the values into the formula: [ \begin{align*} A&=9500\left(1 +\frac{0.04}{4}\right)^{4\times3}\ &=9500(1 + 0.01)^{12}\ &=9500\times(1.01)^{12} \end{align*} ] Using a calculator, $(1.01)^{12}\approx1.12682503$. Then $A = 9500\times1.12682503\approx10704.84$.

Step3: Calculate the additional amount needed

The amount needed to reach $18000$ is $18000 - 10704.84=7295.16$.

Answer:

C. $$7295.16$