Let $1000 be invested at the end of each year in perpetuity. The interest rate is 8% per year. (a) Calculate the present value (PV) of the investment to the nearest cent after : (i) 1 year (ii) 10 years (iii) 50 years (iv) 100 years. (b) Calculate the present value of the perpetuity. Explain why the present values in (a) approach the present value of the perpetuity as the number of years increases.