Question

Noah took out $20,903 in private student loans at 15 percent APR. His cousin Ava took out the same amount of student loans, but she got a federal student loan with an APR of 4.75 percent. What is the difference in the amounts Noah and Ava will pay for their student loans (over 10 years), assuming the interest starts accumulating on the same day? Click on the table icon to view the Monthly Installment Loan Payment Factor (MILPF) table.

Answer 1

Noah: Borrowing = $ 19923, Tenure = 10 years or (10 x 12) = 120 month, APR = 15 %

Applicable Monthly Rate = 15/12 = 1.25 %

Let the monthly repayments be $ M

Therefore, 19923 = M x (1/0.0125) x [1-{1/(1.0125)^(120)}]

19923 = M x 61.9828

M = 19923 / 61.9828 = $ 321.428

Total Amount Paid = 321.428 x 120 = $ 38571.3

Ava: Borrowing = $ 19923, Tenure = 10 years or (10 x 12) = 120 month, APR = 4.5 %

Applicable Monthly Rate = 4.5/12 = 0.375 %

Let the monthly repayments be $ N

Therefore, 19923 = N x (1/0.00375) x [1-{1/(1.00375)^(120)}]

19923 = N x 96.4893

N = 19923 / 96.4893 = $ 206.479

Total Amount Paid = 206.479 x 120 = $ 24777.5

Difference = 38571.3 - 24777.5 = $ 13793.9