Sam has borrowed $150,000 and spent all that money on a car. Sam is being charged 1% per month effective on his loan. To repay this loan, he has agreed to make 12 half-yearly-end payments of $18,000 as well as a smaller 13th payment 6 months after the final $18,000 payment (explicitly, he will repay his loan after 6.5 years). The first $18,000 payment occurs exactly 6 months from today.

a) Calculate the effective half-yearly rate for Sam's loan.

b) Draw a cash flow diagram for Sams loan as described above. Then calculate the size of the extra smaller repayment.

c) Calculate the loan outstanding after 1 year using the retrospective method. Calculations done using the prospective method will score 0 marks.

d) The loan outstanding after 2 years is $111,539.33 (for the purposes of part d), use this rounded value). Using this value and your answer to part c), calculate the total principal and interest repaid by Sam over the second year.