Michael wants to save in order to buy a house in 4 years which he estimates will cost $225,000. He has several sources of funds:
I. His parents will give him $1,000 per quarter starting in 3 months, which will be deposited into an account paying 5% compounded quarterly.
II. He will receive $5,000 from his Aunt's estate in one year's time which will be deposited into the same account as above.
III. He currently has $15,000 cash in a bank account (same as above).
IV. He will take out a mortgage at the time of purchase on which he'll make monthly payments of $1,000 over a 20 year amortization. He expects the interest rate on the mortgage at the time to be 4%.
a) Calculate how much more Michael will need to have in 4 years in order to be able to purchase the house.
b) To make up the shortfall, Michael will make monthly contributions to his investment account which earns 6% compounded annually. How much must he save each month to have enough to buy the house in 4 years' time?