if a savings account of $4200 is compounded quarterly at 16.21% annual interest, how much will the account…

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

The principal $P=$4200$, the annual interest rate $r = 16.21%=0.1621$. Since it is compounded quarterly, $n = 4$. The time $t=\frac{38}{12}$ years.

Step3: Substitute the values into the formula

$A=4200(1 +\frac{0.1621}{4})^{4\times\frac{38}{12}}$ First, calculate $\frac{0.1621}{4}=0.040525$. Then $1+\frac{0.1621}{4}=1 + 0.040525=1.040525$. Next, calculate $4\times\frac{38}{12}=\frac{38}{3}\approx12.67$. So $A = 4200\times(1.040525)^{\frac{38}{3}}$. $(1.040525)^{\frac{38}{3}}\approx(1.040525)^{12.67}$. Using a calculator, $(1.040525)^{12.67}\approx1.6977$. Then $A = 4200\times1.6977=$7130.34$.

Answer:

$7130.34$