a principal amount of $14,390 is placed in a savings account with an annual interest rate of 4.13%…

Explanation:

Step1: Identify 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. Here, $P=$14390$, $r = 0.0413$ (since $4.13%=0.0413$), $n = 12$ (compounded monthly), and $t = 21$.

Step2: Calculate the value of $(1+\frac{r}{n})^{nt}$

First, calculate $\frac{r}{n}=\frac{0.0413}{12}\approx0.00344167$. Then, $nt=12\times21 = 252$. So, $(1+\frac{r}{n})^{nt}=(1 + 0.00344167)^{252}$. Using a calculator, $(1 + 0.00344167)^{252}\approx2.3897$.

Step3: Calculate the final amount $A$

$A=P(1+\frac{r}{n})^{nt}=14390\times2.3897\approx34204.08$.

Step4: Calculate the interest earned

The interest earned $I=A - P$. So, $I = 34204.08-14390=$19814.08\approx$19814.06$.

Answer:

A. $19,814.06$