investing nancy deposits $2500 into an investing account that pays 6.1% annual interest compounded…

Explanation:

Step1: Identify the 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 the given values to the appropriate form

We are given that $P=$2500$, $r = 6.1%=0.061$, $n = 4$ (compounded quarterly), and $t = 10$ years.

Step3: Substitute the values into the formula

$A=2500(1 +\frac{0.061}{4})^{4\times10}$. First, calculate the value inside the parentheses: $\frac{0.061}{4}=0.01525$, and $1 + 0.01525=1.01525$. Then, calculate the exponent: $4\times10 = 40$. So, $A = 2500\times(1.01525)^{40}$.

Step4: Calculate $(1.01525)^{40}$

Using a calculator, $(1.01525)^{40}\approx1.82777$.

Step5: Calculate the value of $A$

$A=2500\times1.82777 = 4569.425$. Rounding to the nearest cent, $A\approx$4569.43$.

Answer:

$4569.43$