Question

Matt needs to borrow money to go to college. He has been granted a student loan of $7000. When is school, he actually only needed $6000. He has two options for paying it back. The great news about student loans is that interest does not calculate until he finishes school. What should be choose and why? • Option A: Pay back $1000 extra before the interest starts. Pay back the $6000 loan over 3 years at 5.2% interest compounded annually by making monthly payments. • Option B: Use the extra $1000 to help buy a car. Pay back the entire student loan over 4 years at 5.2% interest compounded annually by making monthly payments.

Answer 1

Option 1: Payback = $ 1000, Borrowing = $ 6000, Interest Rate = 5.2 % and Repayment Tenure = 3 years or (3x12)=36 months

Applicable Monthly Rate = 5.2/12 = 0.4333 %

Let the monthly repayments be $ M

Therefore, 6000 = M x (1/0.004333) x [1-{1/(1.004333)^(36)}]

6000 = M x 33.2661

M = 6000 / 33.2661 = $ 180.364

Option 2: Borrowing = $ 7000, Interest Rate = 5.2 % and Repayment Tenure = 4 years or (4x12)=48 months

Applicable Monthly Rate = 5.2/12 = 0.4333 %

Let the monthly repayments be $ M

Therefore, 7000 = M x (1/0.004333) x [1-{1/(1.004333)^(48)}]

7000 = M x 43.2529

M = 7000 / 43.2529 = $ 161.839

Total Repayment under Option 1 = 36 x 180.364 = $ 6493.09, Interest Paid = 6493.09 - 6000 = $ 493.09

Total Repayment under Option 2 = 48 x 161.839 = $ 7768.26, Interest Paid = 7768.26 - 7000 = $ 768.26

As the student pays less interest under Option 1 as compared to Option2, the student should select Option1.