You are saving for the down payment on a house. The houses in the area you prefer have an average selling price of $450,000 and you need a 10% down payment to ensure your mortgage payments are not too high. You have $30,000 saved that you can invest today at 6.5% (annual compounding).

a) How long before you will have enough for the down payment saved?

b) You want to buy the house sooner. In addition to the $30,000 saved to date, how much would you need to invest each month (into the same investment) in order to have enough for the down payment in 2 years?

c) What would your payments be for part (b) if you made them at the beginning of the month instead of the end?