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Standby power for water utility pumps and other electrical devices is provided by diesel-powered generators. As an alternative, the utility can use natural gas to power the generators, but it will be a few years before the gas is available at remote sites. The utility estimates that by switching to gas, it will save $22,000 per year, starting 3 years from now. At an interest rate of 8% per year, determine the present worth in year 0 of the projected savings that will occur in years 3 through 10.

Respuesta :

TomShelby

Answer:

Present worth of the prjected savings:   100,361.08

Explanation:

we will calculate the present value of a 22,000 dollars annuity for 8 years at 8% discount rate.

(3rd, 4th, 5th, 6th, 7th, 8th, 9th and 10th year = total of 8 years)

Then, we will bring it to present using the lump sum formula.

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

[tex]22000 \times \frac{1-(1+0.08)^{-8} }{0.08} = PV\\[/tex]

PV $126,426.0568

Then we calculate the present value as this is 3 years into the future:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  126,426.06

time   3.00

rate  0.08

[tex]\frac{126426.056761957}{(1 + 0.08)^{3} } = PV[/tex]  

PV   100,361.08

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