Question

One of your customers is delinquent on his accounts payable balance. you’ve mutually agreed to a repayment schedule of $750 per month. you will charge 1.9 percent per month interest on the overdue balance. if the current balance is $18,000, how long will it take for the account to be paid off?

Answer 1

In this problem, we need to find the length of an annuity. We already identified the interest rate, the PV, and the payments.
Using the PVA equation: PVA =C({1 – [1/(1 +r)t]} /r
$18,000 = $750{[1 – (1/1.019) t] / 0.019}
Then solve for t:
1/1.019t= 1 − {[($18,000)/($750)](0.019)}
1/1.019t= 0.544
1.019t= 1/(0.544) = 1.838
t= ln 2.193 / ln 1.019 = 32.34 months or 2.7 in years