Carlos contracted a loan at the bank. He pays back his loan in 3 payments : the first one is $5000 made after one year, the second one of $4000 made two year and a half after he contracted the loan, and the last one, of $3000, made five years after he contracted the loan. The nominal discount rate is d^(2) = 10%.

a) Determine the amount of the loan.

b) If after his first payment,Carlos renegotiates his loan with the bank such that the nominal discount rate is now d^(4) = 8% and his last payment is set to X. Find X