You are thinking of building a new machine that will sve you 2,000 in the first year the machine will then begin to wear out so that the savings decline at a rate of 4% per year forever. What is the present value of the savings if the interest rate is 5% per year? (Hint: this is a growing perpetuity.)

The present value of the savings is $22222.22

Explanation:

A perpetuity is an indefinite series of equal payments made after equal intervals of time and for an unlimited period. A growing perpetuity is a kind of perpetuity whose period payments are not equal and they grow(or decline) at a constant rate each period for an indefinite period of time.

The formula for the present value of a growing perpetuity is attached.

The present value of the savings can be calculated as follows,

Present value = 2000 / (0.05 - (-0.04)

Present value = 2000 / (0.05 + 0.04)

Present value = 2000 / 0.09

Present value = $22222.22

correct, but each time you dont pay the price of the penalty can increase.

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