Question

A loan of $100,000 is made today. This loan will be repaid by 10 level repayments, followed by a final smaller repayment, i.e., there are 11 repayments in total. The first of the level repayments will occur exactly 2 years from today, and each subsequent repayment (including the final smaller repayment) will occur exactly 1 year after the previous repayment. Explicitly, the final repayment will occur exactly 12 years from today. If the interest being charged on this loan is 8.5% per annum compounded half-yearly, and the final smaller repayment is $300, (a) Calculate the loan outstanding exactly 1 year from today.

Answer 1

Interest Rate = 8.5 %, Compounding Frequency: Semi-Annual, Equivalent Annual Interest Rate = [1+(0.085/2)]^(2) - 1 = 0.08681 or 8.681%

Number of Repayments = 11 with 10 being equal in magnitude and the last one being worth $ 300, the first repayment comes in at the end of Year 2

Let the required level payments be $ p

Therefore, 100000 = p x (1/0.08681) x [1-{1/(1.08681)^(10)}] x [1/(1.08681] + 300 / (1.08681)^(12)

1000000 - 110.483 = p x 5.9889

p = $ 16678.86

Loan Outstanding 1-Year From Now = 16678.86 x (1/0.08681) x [1-{1/(1.08681)^(10)}] + 300 / (1.08681)^(11) = $ 108678.79