carson invested $3,900 in an account paying an interest rate of 2.1% compounded monthly. assuming no…

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 have $P = 3900$, $r=0.021$ (since $2.1%=0.021$), $n = 12$ (compounded monthly), and $t = 14$.

Step3: Substitute the values into the formula

$A=3900(1 +\frac{0.021}{12})^{12\times14}$. First, calculate the value inside the parentheses: $\frac{0.021}{12}=0.00175$, and $1+\frac{0.021}{12}=1 + 0.00175=1.00175$. Then, calculate the exponent: $12\times14 = 168$. So, $A = 3900\times(1.00175)^{168}$.

Step4: Calculate $(1.00175)^{168}$

Using a calculator, $(1.00175)^{168}\approx1.3377$.

Step5: Calculate the value of $A$

$A=3900\times1.3377 = 5217.03$. Rounding to the nearest ten dollars, $A\approx5220$.

Answer:

$5220$