martha took out an 8 - year loan of $35,790 to purchase a sports utility vehicle at an interest rate of 6.2%…

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 or borrowed for in years.

Step2: Convert the given values to the appropriate form

The principal amount $P=$35790$, the annual interest rate $r = 6.2%=0.062$, the number of times compounded per year $n = 12$ (since it is compounded monthly), and the time $t = 8$ years.

Step3: Substitute the values into the formula

$A=35790(1 +\frac{0.062}{12})^{12\times8}$. First, calculate the value inside the parentheses: $\frac{0.062}{12}\approx0.005167$, then $1+\frac{0.062}{12}=1 + 0.005167=1.005167$. Next, calculate the exponent: $12\times8 = 96$. So, $A = 35790\times(1.005167)^{96}$. Calculate $(1.005167)^{96}\approx1.61977$. Then $A=35790\times1.61977\approx57960.67$.

Answer:

$57960.67$