$8,200 is invested in an account with a 2.1% interest rate that is compounded quarterly. how much money is…

Answer:

$8373.87

Explanation:

Step1: Identify the compound - interest formula

$A = P(1+\frac{r}{n})^{nt}$ 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 correct form

$P = 8200$, $r=0.021$ (since $2.1%= 0.021$), $n = 4$ (compounded quarterly), and $t = 1$.

Step3: Substitute the values into the formula

$A=8200(1 +\frac{0.021}{4})^{4\times1}$ $A = 8200(1+ 0.00525)^{4}$ $A = 8200\times(1.00525)^{4}$

Step4: Calculate $(1.00525)^{4}$

$(1.00525)^{4}=1.00525\times1.00525\times1.00525\times1.00525\approx1.021191$

Step5: Calculate the final amount $A$

$A = 8200\times1.021191\approx8373.87$