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Actuarial mathematics Billy contracted a loan at the bank. He pays back his loan in 3 payments : the first one is $5000 made after

Actuarial mathematics

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%. 1) Determine the amount of the loan. 2) 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.

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