$4,200 is invested in an account with a 1.4% interest rate that is compounded quarterly. how much money is…

Explanation:

Step1: Identify the 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 form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

Given $P = 4200$, $r=0.014$ (since $1.4%=0.014$), $n = 4$ (compounded quarterly), and $t = 1$.

Step3: Substitute the values into the formula

$A=4200(1 +\frac{0.014}{4})^{4\times1}$. First, calculate $\frac{0.014}{4}=0.0035$. Then $1+\frac{0.014}{4}=1 + 0.0035=1.0035$. And $(1.0035)^{4}\approx1.01407$. So, $A = 4200\times1.01407$.

Step4: Calculate the final amount

$A=4200\times1.01407 = 4259.094\approx4259.09$.

Answer:

$4259.09$