One of your customers is delinquent on his accounts payable balance. You’ve mutu
ID: 2816601 • Letter: O
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 1.20 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.)
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 1.20 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.)
Explanation / Answer
Periods of annuity payments can be computed using formula for PV of annuity as:
PV = P x [1-(1+r)-n/r]
PV = Present value of annuity or current balance = $ 11,000
P = Periodic cash flow = $ 500
r = Rate per period = 1.2 % or 0.012 p.m.
n = Numbers of periods
$ 11,000 = $ 500 x [1-(1 + 0.012)-n/ 0.012]
$ 11,000/$ 500 = 1-(1.012)-n/ 0.012
22 = (1-(1.012)-n)/ 0.012
22 x 0.012 = 1 - (1.012)-n
0.264 = 1 - (1.012)-n
(1.012)-n = 1 - 0.264
(1.012)-n = 0.736
Taking log of both sides and solving for n, we get:
-n x log 1.012 = log 0.736
-n x 0.0051805125 = - 0.13312218566
n = 0.13312218566/0.0051805125
n = 25.69672125 or 25.70 months
Months for account to be paid off are 25.70 months.
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