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A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900 . After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 5% per year.)

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Answer:

Explanation:

This is a time value of money question. It is basically asking you to find the recurring cost savings per year in perpetuity. Therefore, perpetuity formula to use is as follows;

PV of perpetuity = recurring CF /rate

PV = 2900

rate = 5% or 0.05 as a decimal

Next, plug in the numbers to the formula;

2900 = CF / 0.05

Multiply both sides by 0.05;

2900 *0.05 = CF

CF = 145

Therefore homeowner must save at least $145 on water heating costs every year for this to be a sound investment.

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