Answer:
The investor will pay up the rereofitted pumps in a period of 22.52 months.
Explanation:
First, we solve for the amount of profit generate per month:
21,000 gallons a month x $0.09 per gallon = $1,890
Now, we calcualte the time at which an monthly income of 1890 discounted at 2% per month matches a present value of 34,000
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $1,890.00
time n
rate 0.02
PV $34,000.0000
[tex]1890 \times \frac{1-(1+0.02)^{-n} }{0.02} = 34000\\[/tex]
[tex](1+0.02)^{-n}= 1-\frac{34000\times0.02}{1890}[/tex]
[tex] (1+0.02)^{-n}= 0.64021164[/tex]
We use logarithmics properties to solve for n:
[tex]-n= \frac{log0.64021164021164}{log(1+0.02)[/tex]
-22.52006579
n = 22.5200 = 22 and a half month.
