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Question

The cost of tuition at public universities has been steadily increasing for many years. One Midwestern university pledged to keep the tuition constant for 4 years for all students who finished in the top 3% of their class. One such student who liked research planned to enroll at the university and continue there until earning a PhD degree (a total time of 9 years). If the tuition for the first 4 years will be \$7200 per year and it increases by 5% per year for the next 5 years, what is the present worth of the tuition cost at an interest rate of 8% per year?

Solution

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First thing we need to understand is that tuition for the first 4 years will be $\7,200$ per year and for next 5 years it increases by 5%.

This means we have two parts to solve.

First part is about present worth of base annual amount which is equal to $\7,200$ with n = 3. Parameter n = 3, not 4 because the 4th year is part of gradient series.

Because of that, present worth in year 0 of base annual amount will be calculated as follows:

$\\\\P_A = \7,200(P/A,8\%,3) \\\\P_A = \7,200(2.5771) \\\\P_A = \18,555$

Next thing we need to calculate is present worth of gradient series that starts in year 4 and increases by 5% for the next 5 years which means until year 9.

However, because gradient series only starts in year 4 which means, that by calculating it`s present worth we will get amount located in year 3, we must first calculate $P_G$ and only after that use P/F factor with n = 3 to bring calculated gradient amount in year 0.

This should be done as follows:

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