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

(c) Calculate the amount of the level repayments.

Answer 1

p = $ 12521.82

Explanation:

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

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,

`100000 = p*  (1)/(0.0363) * [1-(1)/((1.0363)^(10))] * (1)/((1.0363)) + (270)/((1.0363)^(12))`

100,000 - 176.01 = p x 7.972

p = $ 12521.82