You would like to have

$100,000

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

8%

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

$100,000?

(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

8%.a.

compounded monthly)

(c) Assume it is now the end of Year 10 (i.e. today), you decide to take up a

30-year

fully amortized loan with an annual percentage rate of

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

$100,000

as a deposit, what would the monthly repayments be?