question 7(multiple choice worth 2 points) (a...
question 7(multiple choice worth 2 points) (applications of interest mc) a homeowner is using a personal loan to borrow $18,000 to replace the roof. the loan offers the option of making no payments for the first 12 months, during which the interest is compounded monthly at an annual rate of 4.4%. what is the total account balance at the end of the year? $808.17 $18,792 $18,808.17 $18,809.68
Answer
# Explanation:
## Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.
## Step2: Convert values to appropriate form
Given $P=\$18000$, $r = 0.044$ (since $4.4\%=0.044$), $n = 12$ (compounded monthly), and $t = 1$ year.
## Step3: Substitute values into formula
$A=18000(1 +\frac{0.044}{12})^{12\times1}$.
First, calculate $\frac{0.044}{12}\approx0.003667$.
Then $1+\frac{0.044}{12}=1 + 0.003667=1.003667$.
Next, $(1.003667)^{12}\approx1.0449$.
Finally, $A = 18000\times1.0449=\$18808.17$.
# Answer:
C. $18,808.17$