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Vanessa borrows R1 250000 from the bank in order to buy a new house. The interest rate is $14,4 \%$ per annum compounded monthly. The loan must be paid off in twenty years by means of monthly payments starting one month after the granting of the loan.

(a) Find the monthly payments.

(b) If Vanessa doubles her monthly payment, calculate how long it will take her to repay the loan and what her final payment will be.
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