Question

You value education and you want your child to receive the best possible education. But sending a child to private schools and Ivy League colleges is not cheap. You want to start saving money so that when you child need the money, you can support him/her. The current assumption is you will have your 1st child in 5 years and you wish to have $200,000 in today’s dollars when he/she is 15 years old. Based on current situation, you expect inflation to be stable at 2% in the foreseeable future. Your plan is to put down savings each year and you can save every year an amount that’s 2% more than the previous year. All your savings go to a stock fund that is expected to return 10% annually, of which 1.5% will be dividends and 8.5% will be capital gains. You pay 15% tax on dividend income as you receive them at the end of each year. You re-balance your fund every year, in other words, you sell all your positions and re-invest at the beginning of a new year, so capital gains are also realized every year, you pay 15% tax on capital gains as well. To have enough money for your child’s education in 20 years, how much money do you have to save in the first year?

Answer 1

Let the required amount be A. As we are paying a tax of 15% on dividends, we are getting just 85% of the dividend income. So 1.5% after tax will become = 1.5 x 0.85 = 1.275%. Similarly, the capital gains of 8.5% after tax will become= 8.5 x (1-0.15) = 7.225%. So, the total return becomes = 7.225 + 1.275 = 8.5%.

Now, if I am saving A amount in first year, I will save 1.02A in second year and so on. So, calculating the future value of the amounts, it takes the form of a geometric progression as follows:

200000 = A x (1.085)^19 + A x 1.02 x (1.085)^18 + ....... + A x 1.02^19 x (1.085)^0.

We calculate this by the formula of geometric progression:

200000 = A x 1.085^19 x[1-(1.02/1.085)^20]/[1-(1.02/1.085)]

200000 = A x 55.786

A= 3585.1288