If you get a constant amount of A each year until year infinity, then the present value of that stream of cash flows is:
PV(A) = Sum[A/(1+r)^n, {n,1,Infinity}] = A/r (Formula 1)
The algebraic demonstration would involve the simple use of the geometric series. But if you wanna check, just evaluate the above expression in Mathematica. In any events, the sum of constant flows was
already discounted by dividing the amount you receive each year by the discount rate.
Note: Sum[A/(1+r)^n, {n,1,Infinity}] = lim[A/(1+r) + A/(1+r)^2 + ... + A/(1+r)^n] as n -> Infinity.
Let a person earn A if he goes to a bad school and A + E if he goes to a good school. The present value of the extra amount is:
PV(E) = PV(A + E) - PV(A) = Sum[(A+E)/(1+r)^n, {n,1,Infinity}] - Sum[A/(1+r)^n, {n,1,Infinity}] = Sum[E/(1+r)^n, {n,1,Infinity}].
Of course this can be obtained by simply plugging E in formula (1) above.
Use Mathematica to evaluate Solve[40,000/(1-.04)==(E/.04)*(1/1.04^5),E], you'll get E = 2027.75
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Originally Posted by asquare
Nope -- you have to discount the future earnings as well as the $40,000. In your calculation, you are still forgetting that a $1500 bonus paid in 20 years has a lower PDV than a $1500 bonus paid next year.
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We're talking about a bonus paid in
each year of the next infinite years.