william invested $7,500 in an account paying an interest rate of 6% compounded monthly. 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 values to appropriate form

Given $P=$7500$, $r = 6%=0.06$, $n = 12$ (compounded monthly), and $t = 18$ years.

Step3: Substitute values into the formula

$A=7500(1 +\frac{0.06}{12})^{12\times18}$. First, calculate the value inside the parentheses: $\frac{0.06}{12}=0.005$, and $1+\frac{0.06}{12}=1 + 0.005=1.005$. Then, calculate the exponent: $12\times18 = 216$. So, $A = 7500\times(1.005)^{216}$.

Step4: Calculate $(1.005)^{216}$

Using a calculator, $(1.005)^{216}\approx2.93667$.

Step5: Calculate $A$

$A=7500\times2.93667 = 22025.025$.

Step6: Round to the nearest ten dollars

Rounding $22025.025$ to the nearest ten dollars gives $22030$.

Answer:

$22030$