5. (&pts) a) (Perpetuity) Your sister has just promised to send you pocket money of $500 each month starting next month and she will keep doing it forever. What is the present value of "having such a sister" if monthly interest rate is equal to 10%. b) (Annuity) You are goint to work for 45 year) (from 20 to 65) earning income of $500.000 a year. Then you are going to retire and going to live for another 35 years (till you are 100). Assume that annual interest rate is given by r = 1%. Write down equation that would allow you to determine the maximal constant level of consumption throughout your whole life (80 years). (write down equation that determines PV of income and consumption, but you do not need to calculate C)