$7.$ A customer has contacted a financial adviser to plan for the possibility of buying a flat in four years$$ time given that he doesn$$t have enough money to meet the $20\%$ of the flat$$s price necessary to be granted a mortgage. The customer is hoping to buy the flat in three years$$ time and the following information is available:

o He has savings of $20,000,$ which are currently in a deposit paying $4\%$ p$.$a$.$ compounded monthly, fixed for the three$-$year period;

o He will be able to save $600$ per month for the next $36$ months, which will be deposited in an investment account that pays interest at $4\%$ p$.$a$.$ compounded monthly;

o The mortgage rate expected to be available in three years$$ time is $5\mathrm{.}9\%$ compounded monthly;

o Given the age of the customer and the location of the flat to be bought, he should be able to get at $30-$year mortgage

Required:

i$.$ Calculate the amount accumulated by in three years$$ time and the maximum amount of the mortgage to be taken out.

ii$.$ Calculate the monthly mortgage payment, assuming this maximum amount is borrowed $($rounded to $000$s$)$ and assuming the conditions above.