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25 July, 05:40

You are thinking of building a new machine that will save you $ 1 comma 000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2 % per year forever. What is the present value of the savings if the interest rate is 5 % per year?

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  1. 25 July, 08:42
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    Present Value = $14,285.71

    Explanation:

    Giving the following information:

    You are thinking of building a new machine that will save you $1,000 in the first year.

    The machine will then begin to wear out so that the savings decline at a rate of 2 % per year forever.

    Interest rate = 5%

    We need to use the formula of a perpetual annuity. Because of the wear out, we need to sum it to the interest rate the 2%

    PV = Cf / (i-wear put)

    PV = 1,000 / (0.05 + 0.02) = $14,285.71
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