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?

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