4. [14 marks] (a) [4 marks] Let i be the interest rate per conversion period, c be the number of interest periods in one payment interval and R be the amount of each periodic payment. Let Ac denote the present value of a complex perpetuity. Show that 1 Ac,00 i sai Give the formula for the capitalized cost K of an asset in terms of its original cost F and corresponding complex perpetuity. (b) [5 marks] Ann's house, painted 4 years ago for 1,000, now needs to be repainted. If Ann decides to switch to a better paint from now on, she will only need to paint the house every 8 years. How much did she pay for the better paint if the capitalized cost re- mained the same, given that the effective rate of interest is 5%? Page 3 of 4 (p.t.o.) = 4. [14 marks] (a) [4 marks] Let i be the interest rate per conversion period, c be the number of interest periods in one payment interval and R be the amount of each periodic payment. Let Ac denote the present value of a complex perpetuity. Show that 1 Ac,00 i sai Give the formula for the capitalized cost K of an asset in terms of its original cost F and corresponding complex perpetuity. (b) [5 marks] Ann's house, painted 4 years ago for 1,000, now needs to be repainted. If Ann decides to switch to a better paint from now on, she will only need to paint the house every 8 years. How much did she pay for the better paint if the capitalized cost re- mained the same, given that the effective rate of interest is 5%? Page 3 of 4 (p.t.o.) =