# Quantitative Methods

**Paper , Order, or Assignment Requirements**

Question 1 (40 marks)

You have just opened a savings account which pays weekly interest at a rate of j52 = 5.46% p.a. You wish to accumulate $10,000 by depositing the same amount into the account at end of each week, for 52 weeks.

. a) Illustrate the cash flows associated with this saving scheme as a fully labelled time line diagram.

. b) Determine the required size for the weekly deposit, R.

. c) Describe and apply a sanity check for you answer in part (b).

. d) Construct a sinking fund table for the last three deposits. Describe and apply a sanity check to your table.

You use the $10,000 you have saved as a deposit on a house which costs $205,000. You borrow the remainder from a bank, which you intend to repay with fortnightly repayments of constant size over a period of 25 years, and subject to an interest rate of j26 = 10.92% p.a. The first payment is due a fortnight after you received the borrowed funds.

. e) Illustrate the cash flows associated with this borrowing scheme as a fully labelled time line diagram.

. f) Determine the required size for the fortnightly repayment, R. Describe and apply a sanity check for you answer

. g) Construct an amortization table for the last two deposits. Describe and apply a sanity check to your table.

Immediately after your 25th repayment, the interest rate increases to j26 = 12.48% p.a.

Question 2 (28 marks)

You and your partner urgently need $3600 to repair your car. A friend suggests that you try one of the many payday lenders which have been advertising on TV. After investigating you find two possible options:

Agile Loans advertise interest free loans up to $2000. You and your partner could thus borrow $3600 by each taking out an $1800 interest free loan. Each loan would be subject to an establishment fee (EF) of 20% of the principal, and a weekly service fee (WSF) of 1% of the amount borrowed. The loan would be paid back over a period of 18 weeks, with the first payment occurring one week after the loan is established and you receive the principal. The size of each payment would be (Principal + EF)/18 + WSF. [NB although you are actually taking out two separate loans, in the questions below, you can effectively treat these as one loan of $3600.]

Cashboat Loans advertise loans of $2000 to $5000 with an establishment fee of 12.5% of the principal, and subject to interest j52 = 39.20% p.a. Cashboat loans are paid back over a period of 18 weeks, with the first payment occurring one week after the loan is established and you receive the principal.

- a) Represent the cashflows associated with either of the above loan scenarios as a fully labelled time line diagram. [2 marks]
- b) Determine the size of the weekly payments made by you and your partner if you take out the Agile loan. [2 marks]
- c) Determine the size of the weekly payments made by you and your partner if you take out the Cashboat loan. [5 marks] [2 marks]
- d) Explain which loan is the better option and why is it valid to simply compare weekly payment sizes.
- e) A consumer advocacy organization has suggested that any personal loan with a comparison rate over 50% p.a. is “exploitive”. For each of the two loan scenarios determine the j52 comparison rate. That is, find the j52 rate for a fee free loan of $3600 repaid with 18 weekly payments of the sizes found in parts (b) and (c). [NB Module 1 notes section 4.18 might be a useful resource. In the iterative process, determine i within an accuracy of 0.001%. Show your working for the first two iterations.]
- f) Identify if either of these loans is exploitive.

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