You would like to have $300,000 in 10 years to be used as a down payment to buy a house. You therefore plan to deposit each month an equal sum of money into your bank account, with the bank paying 12% per annum, compounded monthly.

(a) If these deposit amounts will be made at the beginning of each month, how much must you deposit monthly to accumulate $300,000?

(b) Alternatively, you decide to make one large lump sum deposit today instead of monthly deposits, how much should this lump sum deposit be? (assuming the interest rate

12%.a.compounded monthly)

(c) Assume it is now the end of Year 10 (i.e. today), you decide to take up a 25-year fully amortized loan with an annual percentage rate of 6.6% and the repayments are made at the end of each month. If the purchase price of the house is $1,000,000 and you use the accumulated $300,000 as a deposit, what would the monthly repayments be?