Question

Caden Carpenter is a college student applying for a student loan to complete the final year of his degree program. During the application process, Caden decided that he will pay off the student loan in 5 years. A private loan company approves Caden for a $15,000 student loan that has an interest rate of 3.5% compounded monthly over 5 years. Find the total amount Caden will pay over the course of the loan. Round to the nearest cent as needed.

Answer 1

The formula to calculate the total amount paid on a loan with compounding interest is:

A = P(1 + r/n)^(nt)

Where:

A = the total amount paid

P = the principal amount of the loan

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the loan is taken out for

In this case:

A = 15000(1 + 0.035/12)^(12*5)

By using calculator or formula A=P(1+r/n)^(nt) we can find the total amount Caden will pay over the course of the loan is $18,097.11.

Answer 2

Answer: 16,372.80

Explanation:

To find the amount Caden will pay over the 5 years, use the formula below to find the monthly payment.

P=L×i1−(1+i)−n

The amount of the loan needed, L, is $15,000. Since the interest rate is compounded, the interest rate offered is 3.5% per year and the time period is 5 years or 60 months. Substituting the values into the formula and converting the interest rate to the monthly rate yields the following.

PP=15,000×0.035121−(1+0.03512)−60≈$272.88

To get the total payment, multiply the monthly payment by the duration of the loan, 60 months.

$272.88×60=$16,372.80