phoebe invests $13,700 into a savings account with an interest rate of 2.5% that is compounded quarterly…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert values to appropriate form

Given $P=$13700$, $r = 2.5%=0.025$, $n = 4$ (compounded quarterly), and $t = 10$ years.

Step3: Substitute values into formula

$A=13700(1 +\frac{0.025}{4})^{4\times10}$. First, calculate the value inside the parentheses: $\frac{0.025}{4}=0.00625$, then $1+\frac{0.025}{4}=1 + 0.00625=1.00625$. Next, calculate the exponent: $4\times10 = 40$. So, $A = 13700\times(1.00625)^{40}$.

Step4: Calculate $(1.00625)^{40}$

Using a calculator, $(1.00625)^{40}\approx1.282946$.

Step5: Calculate $A$

$A=13700\times1.282946\approx17577.46$.

Answer:

$17,577.47$ (the closest option to the calculated value)