Your three year old daughter may want to enter university 15 years from now and you've decided to establish a fund to provide for her tuition fees for four (4) years of university education. Tuition is current $1500 per year, however, you anticipate that it will rise by approximately 4% per year between now and when your daughter first enters university. Furthermore, you have assumed that tuition will increase by $150/year in each of the last three years of the four year program. You have also assumed that each year's tuition will be due at the beginning of the year (i.e. first tuition fee due at the end of the 15th year). What equal annual amount will have to be set aside at the end of each of the next 15 years in order to able to fund the expected tuition requirements? Assume you can earn 12%, compounded annually, on your savings.

My attempt so far,

Cost of daughters tution for first year,

$\displaystyle F_{1} = 1500(\frac{F_{1}}{P_{1}}, 4\%, 15) = \$2701.42$

second year,

$\displaystyle F_{2} = 2701.42(\frac{F_{2}}{P_{2}}, 4\%, 1) + 150 = \$2959.47$

third year,

$\displaystyle F_{3} = 2959.47(\frac{F_{3}}{P_{3}}, 4\%, 1) + 150 = \$3227.85$

fourth year,

$\displaystyle F_{4} = 3227.85(\frac{F_{4}}{P_{4}}, 4\%, 1) + 150 = \$3506.96$

If I can take the future values of the 2nd, 3rd and 4th year and bring them back to year one I can sum them all and that would be the future value that I need to have by year 15, call it $\displaystyle F_{15}$.

Then,

$\displaystyle A = F_{15}(\frac{A}{F_{15}}, 12\%, 15)$

Should give me the value of payment that must be made for 15 years in order to pay my daughters tuition, correct?

Does anyone see any mistakes in my thought process? Is there a simpler way to arrive at the same solution?

Thanks again!