One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $500 per month. You will charge 1.55 percent per month interest on the overdue balance. If the current balance is $14,500, how long will it take for the account to be paid off?

Here we need to find the length of an annuity. We know the interest rate, the PV, and the payments. Using the PVA equation:

PVA =C({1 – [1/(1 +r)t]} /r)

$14,500 = $500{[1 – (1/1.0155)t] / 0.0155}

Now we solve for t:

1/1.0155t = 1 − {[($14,500)/($500)](0.0155)}

1/1.0155t= 0.5505

1.0155t= 1/(0.5505) = 1.817

t = ln 1.817 / ln 1.0155 = 38.83 months

Account will be paid off in 38.83 months.