aaron invested $210 in an account paying an interest rate of 4.5% compounded quarterly. assuming no deposits…

Explanation:

Step1: Identify 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 given values to appropriate form

The principal $P=$210$, the annual interest rate $r = 4.5%=0.045$, the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 15$ years.

Step3: Substitute values into the formula

$A=210(1 +\frac{0.045}{4})^{4\times15}$. First, calculate the value inside the parentheses: $\frac{0.045}{4}=0.01125$, and $1+\frac{0.045}{4}=1 + 0.01125=1.01125$. Then, calculate the exponent: $4\times15 = 60$. So, $A = 210\times(1.01125)^{60}$.

Step4: Calculate $(1.01125)^{60}$

Using a calculator, $(1.01125)^{60}\approx1.9997$.

Step5: Calculate the final amount $A$

$A=210\times1.9997\approx419.937\approx420$.

Answer:

$420$