13. I have made a careful assessment of my financial needs on retirement, in exactly 30 years time. Taking into account inflation, and my future living expenses on retirement, I calculate that I will need a nest-egg of $1,200,000. I have found a savings scheme which promises a return of 6% per annum, compounded annually. How much (to the nearest cent) will I need to save at the beginning of each year (first instalment starts right now) if I am to accumulate my nest-egg after thirty years?

14. I want to buy a new car, as my old one has just failed its annual inspection. Right now I can only afford to pay $250 per month, but in two years time I should be able to pay $400 per month. A local finance company quoting rates of 12% per annum, compounded monthly, has offered to extend me a five-year loan whereby I pay them $250 at the end of each month for the next two years, and $400 per month for the three years after that. How expensive a car can I afford to buy (to the nearest dollar)?

15. Today is June 1st and I have just deposited $5,000 in a bank account paying a fixed 5% per annum interest rate over the next six months, calculated according to the Actual/360 convention. How much (to the nearest cent) will I be able to withdraw on December 1st?