Question

Jason borrows $10,000 at an e ective annual rate of 8.00% and promises to pay it back over 18 months with equal monthly installments. Out of the eleventh repayment (i.e. the repayment at t=11), how many dollars of the repayment go toward paying the interest portion and how many dollars go toward paying the principal portion?

Answer 1

Borrowing = $ 10000, Effective Annual Rate = 8 %

Monthly Interest Rate = (1.08)^(1/12) - 1 = 0.00643 or 0.643 %

Tenure of Repayment = 18 months and let the equal monthly intsallments be $ K

Therefore, 10000 = K x (1/0.00643) x [1-{1/(1.00643)^(18)}]

10000 = K x 16.9461

K = 10000 / 16.9461 = $ 590.106

In the eleventh payment worth $ 509.106, the portion going towards paying the interest is determined by the portion of original borowing remaining at the end of the 10th month (post the 10th installment payment)

Borrowing Outstanding (Remaining) after Month 10 = PV at the end of Month 10 of the remaining monthly payments = 590.106 x (1/0.00643) x [1-{1/(1.00643)^(8)}] = $ 4587.13

Interest Accrued between Month 10 and Month 11 on the outstanding borrowing = 4587.13 x 0.00643 = $ 29.4952

Therefore, in the 11th Repayment portion going towards interest payment = Interest Accrued on Outstanding Borrowing between end of Month 10 and end of Month 11 = $ 29.4952

Portion going towards principal repayment = 11th Monthly Installment - Interest Accrued = 590.106 - 29.4952 = $ 560.611