Janis has borrowed $100,000 from the bank to buy a rare Pokemon card. Her debatable financial judgement aside, the bank has agreed to lend her this money at an interest rate of 13% p.a. effective. Janis has agreed to repay this loan over 2 years, using 8 level quarterly installments.

The first installment is exactly 3 months from today. Using this information, answer the following questions.

a) State clearly the type of effective rate that should be used in an annuity formula for Janis loan as described above (e.g. effective quarterly rate, effective weekly rate, etc.). Then determine the value of this effective rate. (1 mark)

b) Draw a cash flow diagram for Janis loan described above, and then determine the size of the level repayment for Janis loan. (2 marks)

c) Suppose that Janis first repayment was instead 2 months from today (the payments are still quarterly). Without doing any further calculations, would you expect Janis quarterly repayments to be larger or smaller than the amount calculated in part b)? Justify your answer. (1 mark)

Kurt has criticised Janis decision to invest in Pokemon cards. Instead, he believes that Beanie Babies are a far superior investment. Shockingly, Kurt has borrowed $150,000 (from a different bank) and spent all that money on Beanie Babies. Kurt 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.

Using this information, answer the following questions.

d) Calculate the effective half-yearly rate for Kurts loan. (1 mark)

e) Draw a cash flow diagram for Kurts loan as described above. Then calculate the size of the extra smaller repayment. (2 marks)

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

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

h) BONUS QUESTION Without doing any further calculations, would the principal repaid in the third year be greater than or less than your answer to part g)? Justify your answer. (1 mark)