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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.)

Answer :

Answer: Number of months = 66.87 months

Explanation:

Given that,

Monthly Payment = $500

Interest rate(r) = 1.95% per month

Current Balance = $18,500

Number of months(t) = ?

[tex]Current\ balance = Monthly\ payment\times(\frac{1-present\ value\ factor}{r})[/tex]

[tex]Current\ balance = Monthly\ payment\times(\frac{1-\frac{1}{(1+r)^{t}} }{r})[/tex]

[tex]18,500 = 500\times(\frac{1-\frac{1}{(1+0.0195)^{t}} }{0.0195})[/tex]

[tex]\frac{18,500}{500}\times0.0195=1-\frac{1}{1.0195^{t} }[/tex]

[tex]\frac{1}{1.0195^{t}}=1-0.7215[/tex]

[tex]1.0195^{t}=\frac{1}{0.2785}[/tex]

[tex]1.0195^{t}=3.5906[/tex]

Taking log on both side

t log(1.0195) = log(3.5906)

[tex]t = \frac{0.5551}{0.0083}[/tex]

t = 66.87 months

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