You would like to have $250,000 in 10 years to be used as a down payment to buy a house

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You would like to have $250,000 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 ?$250,000??

(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 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 ?$250,000 as a? deposit, what would the monthly repayments? be?