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

The investor will pay up the rereofitted pumps in a period of 22.52 months.

Step-by-step 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 * (1-(1+r)^(-time) )/(rate) = PV\\`

C $1,890.00

time n

rate 0.02

PV $34,000.0000

`1890 * (1-(1+0.02)^(-n) )/(0.02) = 34000\\`

`(1+0.02)^(-n)= 1-(34000*0.02)/(1890)`

`(1+0.02)^(-n)=  0.64021164`

We use logarithmics properties to solve for n:

-22.52006579

n = 22.5200 = 22 and a half month.