Question

Your daughter will start college one year from today, at which time the first tuition payment of \$58,000$58,000 must be made. Assume that tuition does not increase over time and that your daughter remains in school for four years. How much money do you need today in your savings account, earning 5\%5% per annum, in order to make the tuition payments over the next four years, provided that you have to pay 35\%35% per annum in taxes on any earnings (e.G., interest on the savings)?

Answer 1

Answer: I'll need $2,14,309.02 in my savings account in order to make tuition payments over the next four years.

We follow these steps in order to arrive at the answer:

In this question, we need to take into account that we need to pay 35% as taxes on interest earned.

So even though the interest rate on the deposit is 5%, only $1 - 35% = 65%$ will be available for use.

Hence, effectively the deposit will only earn $0.05*0.65 = 0.0325$ or 3.25% interest after taxes.

We'll compute the the Present Value of the annuity of 58,000 for four years at 3.25% interest in order to determine the amount that is needed today.

The Present Value of an Annuity formula is

$\mathbf{PV_{Annuity}= PMT\left ( \frac{1 -(1+r)^{-n}}{r} \right )}$

Substituting the values in the equation above we get,

$PV_{Annuity}= 58,000\left (\frac{1 -(1.0325)^{-4}}{0.0325} \right )$

$PV_{Annuity}= 58,000\left (\frac{ 0.12008695 }{0.0325} \right )$

$\mathbf{PV_{Annuity}= 58,000 * 3.69 = 2,14,309.02}$