Question

Eli has a loan of $3500.This loan charges 5% interestcompounded annually. What is theamount of interest that Eli will becharged on this loan at the end offour years?(Round to the nearest cent)

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to find the interest

STEP 1: Write the formula for compund interest

$A=P(1+\frac{r}{n})^{nt}$

Where A =final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

STEP 2: Write the given parameters

$P=3500,r=\frac{5}{100}=0.05,t=4,A=?,n=1\text{ since it is compunded annually,}$

STEP 3: Calculate the Amount after 4 years

$\begin{gathered} A=3500(1+\frac{0.05}{1})^{1\times4} \\ A=3500(1.05)^4 \\ A=3500(1.21550625) \\ A=4254.271875 \\ A\approx4254.27\text{ to the nearest cents} \end{gathered}$

STEP 5: Calculate the amount of interest

$\begin{gathered} \text{Interest}=\text{Amount}-\text{Principal} \\ I=A-P \\ A=4254.27,P=3500 \\ I=4254.27-3500 \\ I=754.27 \end{gathered}$

Hence, the amount of interest that Eli will be charged on the loan after 4 years is $754.27 to the nearest cent