$11.$ A friend of yours is interested in purchasing a motor vehicle with at a cost of $$3\mathrm{.}5$ million. The bank has indicated that they are willing to finance $80\%$ of the purchase price at a rate of $12\%$ p$.$a$.$ over $4$ years with equal monthly repayments. Your friend has asked you to

a$.$ Compute the required monthly payments. $($round to the nearest dollar$)(6$ marks$)$

b$.$ Prepare the Loan amortization schedule for the first $4$ months $($round to the nearest dollar$).(5$ marks$)$

c$.$ Determine how much would be required to close the loan after $2$ years. $(4$ marks$)$