MODULE 1 – TOPIC 1 (MATHEMATICS OF FINANCE )
Weight: This question is worth 23 marks out of 100.
On the first of May 2015 Lee and Kim borrowed $250,000 from the Eastside Bank in order to buy an apartment. The loan was to be repaid through 180 monthly payments over a period of 15 years, with the first payment due on the first of June 2015, and each payment being the same size. The interest rate charged by the eastside bank was j 12=5.04% p.a.
a) Illustrate all the cash flows associated with this loan as a fully labelled timeline diagram [2 marks]
b) Determine the size of the monthly payments. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 1b.
c) Describe and carry out two sanity checks on your answer to part b). [2 marks]
d) Determine the size of the outstanding principal immediately after Lee and Kim’s 20 th payment. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 1d. [1 marks]
e) If the interest rate charged by the Eastside Bank increases to j 12 = 5.52% p.a. immediately after Lee and Kim’s 20 th payment, determine how many more payments it will take to pay off the loan, assuming that Lee and Kim don’t change their payment size. [3 marks]
f) Determine the size of the partial payment [3 marks
g) Describe and carry out a strong sanity check on your answer to f). [2 marks]
h) Construct an amortization schedule, showing the last 3 payments (i.e. two full payments and a partial payment). Ensure that you include example calculations for one line of the schedule, and that you show how you got the starting OP for the table. [4 marks
i) Lee and Lim decide that rather than making a partial payment the month after the full payments finished, they would rather make the last full payment large enough to retire the loan then. Determine the size that this larger payment would need to be. Ensure that you explain the logic of the approach. [2 marks]
j) Referring back to question e), determine what the new payment size would need to be if Lee and Kim wanted to retire the debt by May 2030. (i.e. in 160 more months). [3 marks]
Question 2 (11 marks)
JoJo Klum purchases a life insurance policy from BetterLifeCo. JoJo will pay a premium of $125 every week on Friday, and in return their beneficiaries will receive a payment of $1,000,000 on the second Fridays after JoJo dies. BetterLifeCo invests the premiums it receives and expects to earn interest (net of any costs) of j 52 = 10.4% p.a.
a) Illustrate all the cash flows associated with this scenario as a fully labelled timeline diagram. (Include JoJo’s death as an event of the timeline.) [3 marks]
b) If JoJo lives another 25 years, determine the amount that BetterLifeCo will have accumulated from JoJo’s premiums, at the time of JoJo’s death. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 2b. [1 mark]
c) Determine how much this will accumulate to by the time that BetterLifeCo need to make the payout. [2 marks]
d) Thus, explain whether under this scenario insuring JoJo would have been a profitable exercise for BetterLifeCo. [1 marks
e) Determine the minimum time JoJo would have needed to live in order for BetterLifeCo to break even on the policy. [NB this question is a little more difficult and intended to provide a bit of stretch for stronger students because you need to take into account the two week delay to payout after JoJo’s death.] [4 marks]
Question 3 (16 marks)
Priya takes out a loan from the Deep Bay Bank for $30,000 to buy a new Prius. The interest rate changed is j 26 = 7.54% p.a. The loan is to be repaid over 4 years with the first payment due in a fortnight’s 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. [3 marks]
b) Determine the size of the fortnightly payments made during the first year. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 3b. [1 mark
c) Determine the size of the outstanding principal at the end of the first year. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 3c. [1 mark]
d) Determine the size of the fortnightly payments during the P&I phase of the loan. Enter this value to the nearest cent as an answer to “Assignment Module 1 – Milestones” question 3d.[1 mark]
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 j 12 =10.08% p.a. Priya intends to pay off this loan through payments of $300 per month, starting in a month’s 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. [4 marks]
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).
a) [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 j 26 interest rate that Priya is effectively paying on the car loan. [4 marks