# Tony's son, Mark will start college in 8 years. Tuition costs...

Tony's son, Mark will start college in 8 years. Tuition costs $26,000 today, increasing at an annual rate of 6.1%. Tony wants to earn 8.5% annually on his investments. If he makes an initial investment one year from now, and annual additions at the end of each year until Mark starts college, what is the size of the annual (level) investments he must make to fund 4 years of Mark's college education?

Round the answer to two decimal places.

Annual Investment = $13,747.92

It is assumed that fees of the year, is said to be paid at start of the year.

First, we need to find the amount needed at start of the college.

Cost of Tuition in 8 years = Cost of Tuition today * (1 + r)^n

= $26,000 * (1 + 0.061)^8

= $26,000 * 1.6059 = $41,753.84

Amount needed at start of college = [First year's fees / (r - g)] * [1 + r] * [1 - {(1 + g) / (1 + r)}^{n}]

= [$41,753.84 / (0.085 - 0.061)] * [1 - {(1 + 0.061) / (1 + 0.085)}^{4}]

= [$41,753.84 / 0.024] * [1 - 0.9144]

= $1,739,743.32 * 0.0856

= $148,898.71

So, this is the future amount needed at start of college.

Annual Investment = [Amount needed at start of college * r] / [(1 + r)^{n} - 1]

= [$148,898.71 * 0.085] / [(1 + 0.085)^{8} - 1]

= $12,656.39 / 0.9206 = $13,747.92