Question

1. Narelle borrows $600,000 on a 25-year property loan at 4 percent per annum compounding monthly. The loan provides for interest-only payments for 5 years and then reverts to principal and interest repayments sufficient to repay the loan within the original 25-year period. Assume rates do not change.

a) Calculate the monthly repayment for the first 5 years. (CLUE: it is INTEREST ONLY) (2 marks)

b) Calculate the new monthly repayment after 5 years assuming the interest rate does not change. (You need the repayment required to amortise the loan to $0 in remaining 20 years) (2 marks)

c) Calculate the total repayments over the life of the loan. (2 marks)

d) Has she paid more or less than she would have if she took a principal and interest loan at the outset? Demonstrate showing your workings. (3 marks)

e) Why might she choose interest-only loan terms? (2 marks)

2.A 7-year annuity has annual payments of $2,500. The first payment is at the end of year 1. If interest is 5 percent per annum (effective annual rate) for 2 years followed by 6 percent per annum (effective annual rate) for 5 years, what is the future value of this annuity at the end of 7 years? (3 marks)

3. On 1 July 2017, $10,000 was deposited into an account earning interest at 4 percent per annum compounding monthly. $500 is to be withdrawn each month, commencing on 1 July 2018. How many full monthly withdrawals of $500 can be made? (4 marks)

4.Harry wishes to save $15,000 for a holiday in 3 years’ time. Twelve level quarterly deposits will be made into an account, the first deposit being made immediately. The account earns interest at 5 percent per annum compounding quarterly. Calculate the quarterly deposit to reach the target of $15,000 at the end of the 3 years. (3 marks)

Answer 1

Annual rate = 4.00% Compounded monthly 0.33% Hence, Monthly Rate (r)=Annual Rate/12 Loan amount (A) = 600000 Monthly Interest payment for first 5 years = 2000 600000*0.33% = Hence, Monthly Payments of $2000 for First 5 years Number of Periodic Payments (n) = a) (as 20 years left) b) 240 Discount Rate (D) = {[(1+r) ^n] - 1} / [r(1+r)^n] Discount Rate (D) = 165.02186 Loan Payment = Amount / Discount Factor, or P = A/ D Hence, Payment= 3635.882 Hence, Monthly Payments of $3635.88 for next 20 years c) First 5 year Repayments = 2000 * 60 = Next 20 year Repayments = 3635.88 * 240 = 120000 872611.67 Total Repayment = If taken P+lat the start, then 992611.67 d) Annual rate = 4.00% Hence, Monthly Rate (r)=Annual Rate/12 Loan amount (A) = 0.33% 600000 %3D Number of Periodic Payments (n) = Discount Rate (D) = {[(1+ r) ^n] - 1} / [r(1+r)^n] Discount Rate (D) = 300 189.45248 Loan Payment = Amount / Discount Factor, or P = A/D 3167.021 Hence, Payment= Hence, Monthly Payments of $3167.02 for 25 years Total Repayment = 3167.02 * 300 = Hence, reduction in repayment = 950106.31 42505.362 Hence, reduction in repayment by $42505.36