Part B Short Answer Questions (50 marks) (Write your answers in the space provid
ID: 1171476 • Letter: P
Question
Part B Short Answer Questions (50 marks) (Write your answers in the space provided. Show all workings.) Question 1 (10 marks) Sammy borrows $50,000 from his uncle to buy a car Sammy's uncle charges interest at 6% p.a (compounding monthly).The loan must be repaid by equal, month-end repayments over 5 years a) Complete the loan amortisation schedule for first two months of the loan. (4 marks) Month Repayment Loan Loan (beginning of month) $50,000.00 Interest (end of month) 2 b) Sammy expects to receive a bonus from his employer in exactly 12 months' time. There is a 60% chance his bonus will be $50,000, a 30% chance it will be $20,000 and a 10% chance it will be zero. i. Calculate the expected value and the standard deviation of the bonus. (3 marks) Is the expected bonus sufficient to pay out Sammy's loan? Answer this by calculating the loan outstanding immediately after the 12th repayment and comparing it to your answer to T above. i. (3 marks)Explanation / Answer
1) a) Monthly payment = 50000*0.005*1.005^60/(1.005^60-1) = $ 966.64 Month Loan (Beginning of month) Interest Repayment Loan (End of month) 1 60000.00 300.00 666.64 59333.36 2 59333.36 296.67 669.97 58663.39 b) Bonus Chance [p] amount [b] b*p d=b-36000 d^2 d^2*p 50000 0.6 30000 14000 196000000 117600000 20000 0.3 6000 -16000 256000000 76800000 0 0.1 0 -36000 1296000000 129600000 36000 324000000 Expected value = $36,000 Standard deviation = (324000000)^0.5 = $ 18,000 c) Loan outstanding immediately after the 12th repayment = PV of the balance 48 installments = 966.64*(1.005^48-1)/(0.005*1.005^48) = $ 41,159.84 NO, the expected bonus will not be sufficient to repay the loan.