# Quantitative Methods

| August 4, 2016

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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.

1. a) Represent the cashflows associated with either of the above loan scenarios as a fully labelled time line diagram.  [2 marks]
2. b) Determine the size of the weekly payments made by you and your partner if you take out the Agile loan.  [2 marks]
3. 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]
4. d) Explain which loan is the better option and why is it valid to simply compare weekly payment sizes.
5. 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.]
6. f) Identify if either of these loans is exploitive.

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