Question

Your first job out of college will pay you $81,000 in year 1 (exactly one year from today). You estimate that your salary will grow at 7% per year for 44 years (compounded annually), when you'll stop working. If the applicable discount rate is 13%, what is the present value of these future earnings today? Round to the nearest cent.

Step 1

C_{1} = $81,000 in year 1

Salary growth rate, g = 7% per year

C_{2} = C_{1} x (1 + g)

C_{3} = C_{2} x (1 + g) = C_{1} x (1 + g)^{2}

C_{4} = C_{3} x (1 + g) = C_{1} x (1 + g)^{3} and so on.....

N = 44 years after first year = 44 + 1 = 45 years from now

r = discount rate = 13%

Step 2

Present value of future earnings = PV.

Please see the white board.

Step 3

On the RHS, let's make two substitution:

A = C1 / (1 + r) and

R = (1 + g) / (1 + r)

Th...

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