A piano company launches a marketing campaign for its new pianos. There are three different offers provided to its customers:

Plan A: Customers can take a discount of 10% off the marked price, but will need to pay 30% (i.e. to pay $30000) of the marked price at the time of purchase and pay the remaining amount after two months.

Plan B: Customers need to pay 10% (i.e. to pay $10000) of the marked price at the time of purchase and the remaining amount after two months. Under this plan, a cash rebate equal to the initial payment will be given to its customers six months after the pianos are sold.

Plan C: Customers can pay 12% (i.e. $12000) of the marked price now and then by installment. For the installment, 2% (each installment pays $2000) of the marked price has to be paid at the end of each month for 4 years (pay 48 times in 4 years).

John wants to buy a new piano that costs $100,000 from the company. Find the present value of the payment for each plan if the interest rate is 12% per annum compounded monthly, and hence determine the plan that John would choose.

PV = C/r% x [1-1/(1 + r%)^n]