Please answer question 3 (a to c)

3. (a) Calculate the present value of an annuity payable annually in advance for a term of 12 years such that the payment is K3,000 in year 1, K3,500 in year 2, K4,000 in year 3 etc. Assume interest rate of 3% pa for the first 8 years and 5% pa thereafter. (b) A series of 12 payments is received at times 2, 3, 4, .... The first payment is K4,500. Each of the next five payments is 3% greater than the previous one, and the re- mainder increase by 4.79% each time. Find the value of these payments at time 0 using an interest rate of 8% pa effective. Page 2 (c) An investor wishes to find the present value of a stream of property income pay- ments. She proposes to make the following assumptions: The level of current payments is K120,000 pa, paid quarterly in advance. Payments will remain fixed for 9-year periods. At the end of each 9-year period, the payments will rise in line with total inflationary growth over the previous five years. Inflation is assumed to be constant at 2% per annum. The rate of interest for the calculation is 15% per annum effective. Find the present value of the income stream assuming that the payments continue for 63 years. 3. (a) Calculate the present value of an annuity payable annually in advance for a term of 12 years such that the payment is K3,000 in year 1, K3,500 in year 2, K4,000 in year 3 etc. Assume interest rate of 3% pa for the first 8 years and 5% pa thereafter. (b) A series of 12 payments is received at times 2, 3, 4, .... The first payment is K4,500. Each of the next five payments is 3% greater than the previous one, and the re- mainder increase by 4.79% each time. Find the value of these payments at time 0 using an interest rate of 8% pa effective. Page 2 (c) An investor wishes to find the present value of a stream of property income pay- ments. She proposes to make the following assumptions: The level of current payments is K120,000 pa, paid quarterly in advance. Payments will remain fixed for 9-year periods. At the end of each 9-year period, the payments will rise in line with total inflationary growth over the previous five years. Inflation is assumed to be constant at 2% per annum. The rate of interest for the calculation is 15% per annum effective. Find the present value of the income stream assuming that the payments continue for 63 years