Suppose that you borrow a loan of amount P from a bank at the end of month 3 and make the monthly deposits to the bank as in the cash flow diagram below. In the following cash flow diagram A₇=A₈=A₉=1000, and starting with A₁₀, deposits start decreasing in the amount of 40. However, due to a cash problem, you miss a payment at month 12 but continue with your original payment plan thereafter (that is, A₁₀=960, A₁₁=920, A₁₂=0, A₁₃=840 etc). With these payments, your dept to the bank will be 0 at the end of month 20. Assuming that the interest rate is 12% compounded monthly.

a)Find out the initial loan amount P.

b)Find the total interest paid to the bank