Question

A business has taken out a $75,000 loan for a wind system, expecting to pay the annual payments from the savings of generating electricity, which in present dollars amounts to $3500 in savings per year. The loan is at 5.5% rate and the inflation rate of electricity is 10%. How long will it take to pay the loan? Please show all work.

Answer 1

Here Saving in electricity is increses by inflation every year.

Here we use present value of growing annuity concept.

PV of growing annuity = ( p / (r -g)) [ 1 - ( 1+g / 1+r)n ]

75,000 =[ 3500/ (0.055 - 0.10)] [ 1 - ( 1.10 /1.055)n ]

1 - (1.042654028436)n = 75000 / (-77,777.7777)

-(1.042654028436)n = -0.96428571525 - 1

(1.042654028436)n = 1.96428571525

Applying log on both sides then

n log(1.042654028436) = log (1.96428571525)

n = log (1.96428571525) / log(1.042654028436)

n = 16.16323 years