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21 December, 03:21

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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  1. 21 December, 03:27
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    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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