a) Mr Dirk, a young architect of 33, wishes to spend a uniform sum of money at the end of each year when he will retire at the age of 60. Assuming an annual rate of interest of 3.5%, calculate how much lump sum, he has to save by the age of 60 in order to be able to spend $25000 at the end of each year, assuming a life expectancy of 22 years

b) MHC has for a long time been dominating the market for housing loans with an annual rate of interest of 8%. HSBC has recently launched a Rs 3M housing loan of 25 years where the prospective customer pays an Annualised percentage rate of interest of 7.5% compounded on a monthly basis. SBI has also retaliated with the same loan amount and maturity period but with a lower annualised percentage rate of 7.25% compounded on a monthly basis. Assuming you are a prospective customer wishing to acquire the housing loan, calculate the difference in the monthly payment between the HSBC loan and the SBI loan.