Solve these questions clearly.
(1) Calculate the following at i =9% : (a) (b) (c) (@ )100 (d) (ii) Calculate the following at i = 7% : (a) (/s) (b) (/5 ) 101 A series of payments is to be received annually in advance. The first payment is f10. Thereafter, payments increase by $2 per annum. The last payment is made at the beginning of the tenth year. Determine whether each of the following is a correct expression for the present value of the annuity. (i) But + 2 Et 1=0 1 = 0 (ii) 10ago + 2(/alg] [iii) 8#10 + 2(/@)10 3 Given that o(t) =0.01t for Ost= 10, calculate the value of (/a)10] An annuity is payable annually in advance for a term of 20 years. The payment is $500 in year 1, ityle 6550 in year 2, and so on, increasing by $50 each year. Calculate the present value of this annuity, assuming that the effective rate of interest is 5% pa for the first twelve years and 7% po thereafter. [5] 5 A continuous payment stream is such that the level rate of payment in year t is 100x1.05-1, for t=1,2,...,10. Calculate the present value of this payment stream as at its commencement date, assuming a rate of interest of 10% pa.6 A series of 10 payments is received at times 5, 6, 7,..., 14. The first payment is $200. Each of the next five payments is 5.7692% greater than the previous one, and thereafter each payment is 6.7961% greater than the previous one. Calculate the present value of these payments at time 0 using an interest rate of 10% po effective. 7 An investor in property expects to receive rental payments for the next 50 years in line with the tyic following assumptions: The current level of rental payments is f20,000 per annum, paid quarterly in advance. Payments will remain fixed for 5-year periods. At the end of each 5-year period the payments will rise in line with total inflationary growth over the previous five years. Inflation is assumed to be constant at 3% per annum. The interest rate is 12% per annum effective. Calculate the present value of the rental income the investor expects to receive. [6] 8 (1) Assuming a rate of interest of 6% po effective, calculate the present value as at 1 January style 2020 of the following annuities, each with a term of 25 years: (a) an annuity payable annually, where the first payment is $3,000 made on 1 January 2021, and payments increase by $500 on each subsequent 1 January. (b) an annuity as in (i), but only 10 increases are to be made, the annuity then remaining level for the remainder of the term. [5] (ii) An investor is to receive a special annual annuity for a term of 10 years in which payments are increased by 5% compound each year to allow for inflation. The first payment is to be f1,000 on 1 November 2021. Calculate the accumulated value of the annuity payments as at 31 October 2038 if the investor achieves an effective rate of return of 4% per half-year. [4] [Total 9]
