Question

It costs ​$34,000 to retrofit the gasoline pumps at a certain filling station so the pumps can dispense E85 fuel​ (85% ethanol and​ 15% gasoline). If the station makes a profit of ​$0.09 per gallon from selling E85 and sells an average of 21,000 gallons of E85 per​ month, how many months will it take for the owner to recoup her ​$34,000 investment in the retrofitted​ pumps? The interest rate is 2​% per month.

Answer 1

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

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $1,890.00

time    n

rate 0.02

PV $34,000.0000

$1890 \times \frac{1-(1+0.02)^{-n} }{0.02} = 34000$

$(1+0.02)^{-n}= 1-\frac{34000\times0.02}{1890}$

$(1+0.02)^{-n}= 0.64021164$

We use logarithmics properties to solve for n:

$-n= \frac{log0.64021164021164}{log(1+0.02)$

-22.52006579

n = 22.5200 = 22 and a half month.