QUESTION 3

(The formulas, values and hints are given in parts 3b , 3c and 3d. Kindly give correct answers for all parts.) Priya takes out a loan from the Deep Bay Bank for $30,000 to buy a new Prius. The interest rate changed is j26 = 7.54% p.a. The loan is to be repaid over 4 years with the first payment due in a fortnights time. The terms of the loan are that it is an interest only loan for the first year (first 26 payments), at which time it converts to a fully amortized P&I loan.

a) Illustrate all the cash flows associated with this scenario as a fully labelled timeline diagram. b) Determine the size of the fortnightly payments made during the first year. Enter this value to the nearest cent. (The formula in this question is: principal * i). c) Determine the size of the outstanding principal at the end of the first year. Enter this value to the nearest cent. (Hint : as interest is only paid in the first year hence, the outstanding principal stays the same as first year is only interest pay period.)

d) Determine the size of the fortnightly payments during the P&I phase of the loan. Enter this value to the nearest cent. (Formula to use in this question is: PV = R (1-(1 + i)) / i). (PV = Present Value, R = amount of the periodic payment, i = the interest rate so 7.54% / 26, n = number of payments or also compounding periods.) At the same time that Priya takes out the loan for the car, she also takes out a second loan for $10,000 from the Mountain River Bank in order to pay off her credit card debit. The Mountain River Bank change interest at a rate of j12 =10.08% p.a. Priya intends to pay off this loan through payments of $300 per month, starting in a months time, until the loan is paid off. e) Find the total Priya owes (i.e. across both loans) two years after she took out the loans. f) Given that most banks (including the Deep Bay Bank and the Mountain River Bank) have similar cost structures and similar investment options, explain a plausible reason why the Deep Bay Bank may have been able to offer a much lower interest rate on the car loan than the Mountain River Bank could for the credit card loan. (50 to 100 words). g) [Tricky bit for stronger students.] The Deep Bay Bank charges a fee of $600 to convert the loan from an interest only loan to P&I loan, and this fee is paid at the same time as the first payment on the P&I loan. That is, payment number 27 rather than being R is actually R+600. Determine the j26 interest rate that Priya is effectively paying on the car loan. [Hints: You could attempt this as a find i price is right approach as outlined in the notes, although it will be a fair bit of work for four marks. Alternatively, you could do a little research on Internal Rate of Return, and in particular on Excels IRR function. The IRR that the bank achieves on the loan will be the same as the interest rate that Priya is effectively paying.]