Billy 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%. Draw a time line a) Determine the amount of the loan. b) If after his first payment, Billy 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.