Question

Suppose that a young couple has just had a baby boy, and they wish to have enough saved to fund four years of college education at a school like UCLA when their son is at the ages of 19-22. Suppose this year’s total expense of an undergraduate student at WashU, including tuition, room and board, books and supplies, amounts to $74,000. This annual cost is expected to grow at 3.5% a year. To simplify the timeline, they assume that all the expenses will be paid in full on their child’s birthdays while he is in college, that is, his 19th to 22nd birthdays. The annual return expected on a college savings account is 8%. How much do they need as of today in order to fund their child’s college education?

Answer 1

Annual expenses of an undergraduate student currently $74,000, which is expected ti grow at 3.5% annually. Hence,

at the end of 19th year the amount required will be:

P * (1+i)n

Where P = principal amount, i = rate of interest and n= number of periods.

= $74,000 (1+ 0.035)¹⁹

= $74,000 * 1.922

= $1,42,265

at the end of 20th year

= $74,000 (1+ 0.035)²⁰

   $74,000 * 1.9897

= $1,47,238

at the end of 21st year

= $74,000 (1+ 0.035)²¹

= $74,000 * 2.0594

= $1,52,395

at the end of 22nd year

= $74,000 (1+ 0.035)²²

= $74,000 * 2.131

= $1,57,694‬

$1,42,265 + $1,47,238 + $1,52,395 + $1,57,694‬ = $5,99,862

They would require $1,42,265 for his 19th birthday, $1,47,238 for 20th, $1,52,395 for 21st and $1,57,694‬ for 22nd. Therefore Total of $5,99,862 would be required. In order to know how much they would need today, PV of each year's requirement will be calculated as follows:

at the end of 19th year

PV = A * 1 / (1+i)ⁿ

= $1,42,265 * 1 / (1+0.08)¹⁹

= $1,42,265 * 0.2317

= $32,964

at the end of 20th year

= $1,47,238 * 1 / (1+0.08)²⁰

= $1,47,238 * 0.2145

= $31,583

at the end of 21st year

= $1,52,395 * 1 / (1+0.08)²¹

= $1,52,395 * 0.1986

= $30,265

at the end of 22nd year

= $1,57,694‬ * 1 / (1+0.08)²²

= $1,57,694‬ * 0.1839

= $29,050

Hence, the parents would require $32,964 for his 19th birthday, $31,583 for 20th, $30,265 for 21st and $29,050 ‬for 22nd. Therefore Total of $1,23,862 would be required in terms of Present Value.