$1.$ Southern Pacific Ltd is contemplating the purchase of a new machine. The total cost of the machine is $$120000,$ and the firm plans to pay a deposit of $$20000.$ The balance would be financed by loan. The firm$$s bank has offered two alternative repayments plans, both at a rate of $14\%$ annually. Plan A involves equal instalments payable at the end of each of the next four years. Plan B requires four equal annual payments at the end of each year plus a balloon payment of $$20000$ at the end of year $4.$

a$.$ Compute annual instalment on plan A

b$.$ Compute annual instalment on plan B

c$.$ Illustrate how the loan amortises on plan A using the amortisation schedule