Well, how about just doing the algebra? He borrowed $10000 at 8% interest so his interest for the first year is (.08)(10000)= $800. At the end of the first year he owes $10800. If his annual payment is P, after that payment, he still owes 10800- P.
How much will the interest be for the second year? Add that to the 10800-P he owed to get how much he owes before his payment. How much will he owe after his annual payment?
Now do that for the third, fourth, and fifth years. Set the amount still owed after his fifth annual payment to 0 and solve for P.
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