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 3.6% per annum compounded half-yearly, and the final smaller repayment is $270,

(c) Calculate the amount of the level repayments.

Interest Rate = 3.6 %, Compounding Frequency: Semi-Annual, Equivalent Annual Interest Rate [tex]= [1+\frac{0.036}{2}]^(2) - 1 = 0.0363 or 3.63[/tex] %

Number of Repayments is 11 with 10 being equal in magnitude and the last one being worth $ 270, the first repayment comes at the end of Year 2

Let $ p be the level payments that required. Therefore,

[tex]100000 = p\times \frac{1}{0.0363} \times [1-\frac{1}{(1.0363)^{10}}] \times \frac{1}{(1.0363)} + \frac{270}{(1.0363)^{12}}[/tex]

100,000 - 176.01 = p x 7.972

p = $ 12521.82