2. Time value of money: Katie and Pete McDonald are preparing to purchase their first house and have managed to save some money. However, although they have these funds, they still need to come up with more money to make up 20% of the deposit, which amounts to $30,000. After much discussion with their family, they have come up with these two possible options:

Option 1 - Borrow money from Katies aunt, Patricia.

Option 2 - Petes Dad, Jason, will take out a loan on their behalf. Ignore any transaction costs and tax involved in buying a house. Required:

(a) Option 1 Patricia (Katies aunt): Using the relevant interest factor table, calculate the following (round your answers to two decimal places): (i) Katies aunt, Patricia, has offered to lend them the $30,000 and she is happy for the loan and interest to be repaid 10 years later. If Katie and Pete borrow the money from Patricia, they will have to repay the amount of $48,870 (which includes the principal amount of the loan and the interest). What rate of interest, compounded annually, would Katie and Pete be paying on the 10-year loan? How much interest would they have paid on the loan?

(ii) If Patricia asks Katie and Pete to repay the loan as an annual equal amount at the end of each year over the 10-year period based on the annual rate of interest calculated from a(i), how much would the annual repayment be? What is the total cash repayment for the loan over the period? How much interest would they have paid on the loan?

(b) Option 2 Jason (Petes Dad). Using the relevant interest factor table, calculate the following (round your answers to two decimal places):

(i) Jason is willing to borrow the $30,000 from his bank (Westman Bank) on their behalf with an interest rate of 8% p.a. compounding quarterly. The loan and the interest are to be repaid 5 years later. If Jason borrows the money from the bank, how much will he pay the bank in 5 years time?

(ii) Jason decided to find out from another bank (BSB Bank) under what conditions they were willing to lend the money to him. If he borrowed $30,000, they would charge an interest rate of 4% p.a. compounded semi-annually. The loan and interest will have to be repaid to the bank over the 5 years with equal payments needing to be made at the beginning of each period. If Jason borrows the money from this bank, what will be the semi-annual payments that he will make? What is the total cash repayment for the loan over the period? How much interest would he have paid on the loan?

(c) Based on your answers to the above questions for options 1 and 2, make a recommendation to Katie and Pete as to which option they should choose and explain why?

(d) What factors should Katie and Pete consider before making a decision to take out a mortgage to buy their first home? Discuss and ensure that your answer relates to the current New Zealand environment.