marcus receives an inheritance of $6,000. he decides to invest this money in a 20 - year certificate of…

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

We have $P = 6000$, $r=0.055$ (since $5.5%= 0.055$), $n = 12$ (compounded monthly), and $t = 20$.

Step3: Substitute values into the formula

$A=6000(1 +\frac{0.055}{12})^{12\times20}$. First, calculate the value inside the parentheses: $\frac{0.055}{12}\approx0.0045833$, then $1+\frac{0.055}{12}=1 + 0.0045833=1.0045833$. Next, calculate the exponent: $12\times20 = 240$. So, $A = 6000\times(1.0045833)^{240}$. Using a calculator, $(1.0045833)^{240}\approx3.004027$. Then $A=6000\times3.004027 = 18024.162$.

Answer:

$18024.16$