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net benefit of a college education

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A high school graduate is considering whether to attend college. He predicts that his earnings, if she doesn't attend college, will be $25,00 per year (real). he predicts that his earning after four years of college will be $37,000. tuition costs are $5,000 per year. assume that college begins at age 18 and ends at age 22, and that he will work until age 65.

a. Write out the equation used to evaluate the net benefit of a college education, for discount rate r.

b. If the discount rate is 5%, what is the value of the net benefit (which could be positive or negative) of a college education?

c. What is the internal rate of return for the college investment that this person faces?

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a. write out the equation used to evaluate the net benefit of a college education, for discount rate r.

Present value of earnings without college education is the Sum of PV of annuity 25000 for 65-18 = 47 years
PV1 = ∑25000/(1+r)^t where t = 1, 2, ... , 47
PV1 = 25000*[1/(1+r) + 1/(1+r)^2 + ... + 1/(1+r)^47]
Multiply both sides by 1/(1+r), then
1/(1+r) PV1 = 25000*[1/(1+r)^2 + 1/(1+r)^3 + ... + 1/(1+r)^48]
Then PV1 - 1/(1+r) PV1 = 25000*[1/(1+r) + 1/(1+r)^2 + ... + 1/(1+r)^47] - 25000*[1/(1+r)^2 + 1/(1+r)^3 ...

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In the following posting, help is given to evaluate the net benefit of a college education.

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