Q3. (a) Nine years ago a family incurred a 20-year RM90,000 mortgage at 8% effective on which they were making annual payments. They desire now to make a lump-sum payment of RM5000 and to pay off the mortgage in nine more years. Find an expression for the revised annual payment if the lender is satisfied with an 8% yield for the past nine years but insists on a 9% yield for the next nine years.(3 marks)(b) Encik Ramli borrows RM20,000 and will repay the loan under a 25-year annuity immediate payments. The annual repayment is calculated at an effective interest rate of 8% with increment of RM50 each year.

(i)Calculate the amount of the first payment.(3 marks)

(ii)Calculate the outstanding balance after the first three payments have been made.(3 marks)

(iii) Explain your answer to part (ii)(3 marks)

(iv) Calculate the total amount of interest paid over the term of the loan.(3 marks)

(c) Describe the characteristics of a repayment loan (or mortgage).(3 marks)

(d) A fund purchased an office block nine months ago for RM5 million. It will spend a further RM900,000 on refurbishment in two months' time.

A company has agreed to occupy the office block six months from now. The lease agreement states that the company will rent the office block for fifteen years and will then purchase the property at the end of the fifteen year rental period for RM6 million. It is further agreed that rents will be paid at the beginning of each quarter and will be increased every three years at the rate of 4% per annum. The initial rent has been set at RM200,000 per quarter with the first rental payment due immediately on the date of occupation.

Calculate, as at the date of purchase of the office block, the net present value of the project to the fund assuming an effective rate of interest of 8% per annum.