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 1.95 percent per month interest on the overdue balance.

Problem 6-21 Calculating Number of Periods [LO3]

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 1.95 percent per month interest on the overdue balance.

If the current balance is $18,500, how long will it take for the account to be paid off? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The time line is:

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)

$18,500 = $500{[1 – (1/1.0195)t]/.0195}

Now we solve for t:

1/1.0195t = 1 − {[($18,500)/($500)](.0195)}

1/1.0195t = .2785

1.0195t = 1/.2785 = 3.591

t = ln3.591/ln1.0195

t = 66.19 months

   

Calculator Solution:

  

Enter

1.95%

$18,500

±$500

N

I/Y

PV

PMT

FV

Solve for

66.19