One of your customers has just made a purchase in the amount of $12,000. You have agreed to payments of $290 per month and will charge a monthly interest rate of 0.84 percent. How many months will it take for the account to be paid off?

It will take 51 months.

Explanation:

As we know the constant payment of $290 monthly is the annuity payment to pay $12,000 with interest rate of 0.84% per  month. The Number of Months can be calculated by following formula.

Loan amount = PV = $12,000

Rate of interest = r = 0.84 %

Monthly Payment = P = $290

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

$12,000 = $290 x [ ( 1 - ( 1 + 0.84% )^-n / 0.84% ]

$12000 x 0.84% / $290 = 1 - ( 1 + 0.84% )^-n

0.347586 = 1 - ( 1 + 0.84% )^-n

0.347586 - 1 = - ( 1 + 0.84% )^-n

-0.652414 = - ( 1 + 0.84% )^-n

1 / 0.652414 = 1.0084^n

1.532769 = 1.0084^n

Log 1.532769 = n x log 1.0084

n = Log 1.532769 / log 1.0084

n = 51

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