Question

Consider a student loan of $17, 500 at a fixed APR of 12 % for 15 years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Answer 1

This is an EMI problem

(a)

The mathematical formula for calculating EMIs is: EMI = [P x R x (1+R)^N]/[(1+R)^N-1],

where P stands for the loan amount or principal = 17500

R is the interest rate per month = 12%/12 = 1% monthly

N is the number of monthly instalments = 15*12 = 180

EMI = [17500 x 0.01 x (1+0.01)^180]/[(1+0.01)^180-1] = $210.03

so monthly payment is $210.03

(b)

Total amount paid = no. of monthly payments x monthly payment = 180*210.03 = $37,805.29

total amount paid is $37,805.29

(c)

Prinicpal paid = 17500

% of the total amount paid as principal = $17500/ $37,805.29 = 46%

% of the total amount paid as interest = Rest of the amount = 100% - 46% = 54%