Question

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 1.2 percent per month interest on the overdue balance.
If the current balance is $11,000, 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.)

Answer 1

Answer:

It will take approximately 25.70 months for the the account to be paid off.

Explanation:

Assuming the customer pays at the end of every month, the relevant formula to use is therefore the formula for calculating the present value of an ordinary annuity as follows:

PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)

Where;

PV = Present value or current balance = $11,000

P = Monthly repayment = $500

r = interest rate = 1.2%, or 0.012

n = number of months = ?

Substitute the values into equation (1) and solve for n, we have:

11,000 = 500 * [{1 - [1 / (1 + 0.012)]^n} / 0.012]

11,000 / 500 = {1 - [1 / (1 + 0.012)]^n} / 0.012

22 * 0.012 = 1 - 0.988142292490119^n

0.264 =  1 - 0.988142292490119^n

0.988142292490119^n = 1 - 0.264

0.988142292490119^n = 0.736

Loglinearizing both sides, we have:

n * log (0.988142292490119) = log (0.736)

n = log (0.736) / log (0.988142292490119)

n = -0.133122185662501 / -0.00518051250378013

n = 25.70

Therefore, it will take approximately 25.70 months for the the account to be paid off.