Answer:
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
