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 3.0% per annum compounded half-yearly, and the final smaller repayment is $310,

(a) Calculate the loan outstanding exactly 1 year from today.

(b) Calculate the loan outstanding exactly 11 years from today.

(c) Calculate the amount of the level repayments.