Answer:
It will take 98 months to pay-off the loan
Explanation:
We need to solve for time (n) in a given annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $60.00
time n
rate 0.011583333 (0.139 annual / 12 months)
PV $3,500.0000
[tex]60 \times \frac{1-(1+0.0115833)^{-n} }{0.0115833} = 3500\\[/tex]
[tex](1+0.0115833)^{-n}= 1-\frac{3500\times0.0115833}{60}[/tex]
[tex](1+0.0115833)^{-n}= 0.32430556[/tex]
now, we use logarithmics properties to solve for n:
[tex]-n= \frac{log0.324305}{log(1+0.011583)}[/tex]
-n = -97.77655542
n = 97.77 = 98
