2. Time value of money: 21 marks Megatron is interested in buying a house as his kind uncle Fallen has offered to provide him with a 20% deposit as a gift. Megatron is an engineer in the aviation industry and earning a good salary as a result of an ingenious invention therefore is able to apply for a mortgage. Megatron has been making enquiries for a mortgage provider and been given several offers. The house that he is interested in will cost $1,000,000. The mortgage offers are as follows: Bank 1: Annual payments of $51,200 and the mortgage will be repaid in 25 years. Bank 2: Annual payments of $69,750 and the mortgage will be repaid in 20 years. Bank 3: Annual payments of $77,070 and the mortgage will be repaid in 15 years. Ignore transaction costs and tax of buying a house. Assume all payments are made at the end of the year. Required:

(a) (i) Using the relevant present value table, calculate (round your answers to the nearest whole number): a. The interest rate that has been applied to each of the mortgage offers? b. The total repayments made over the life of each mortgage? and c. The amount of interest that will be paid for each mortgage? (12 marks)

(ii) Which bank will Megatron choose? (1 mark)

(iii) Using your answer in (a)(ii) above, supposing Megatron increased both his deposit and annual payments by 5% how would that change the length of the mortgage assuming the interest rate stayed the same. Show your calculation. (3 marks)

(b) Any investment carries with it an element of risk. If Megatron decided against buying a house he could instead invest the money promised by his uncle in a savings account. Calculate the interest rate (to two decimal places) that Megatron would need to earn to grow the money promised by his uncle to $1,000,000 - use the period of the mortgage you determined to adopt in (a)(ii). (Ignore the information in (a)(iii)). (3 marks)

(c) If Megatron decided against buying a house he could instead invest the money promised by his uncle in a new New Zealand based high technology company with terrific prospects operated by a school friend that is not listed on the stock exchange. Provide an example of a risk and a benefit associated with this option. (2 marks)