Question

You and your significant other are going to have a baby one year from now.

Of course your little pride-and-joy is going to be cute AND smart. After much consultation, your significant other and you have decided that you want the little one to go to a private four-year college in the United States. However, private colleges are very expensive. The average current cost is estimated to be around $43,921 per year, including tuition, fees, room, and board. You expect these costs to increase by 3% per year beyond the current annual rate of inflation of 2%.

Your child will most likely begin college eighteen (18) years after birth. Colleges tend to demand payment of the annual cost at the beginning of each year. You expect to invest your money in a manner that returns 7.50% per year over the foreseeable future. You want to start saving soon. In fact, you plan to invest money every year. To be precise, you will put away money once a year, starting when the baby is born, and ending one year prior to the beginning of your child’s first year in college.

A. Suppose you want to save the same (constant) amount each year in nominal dollars. How much will you have to save each year so that there is enough money to send your child to college?

B. (13 points) Now suppose that you want to save a constant percentage of your salary every year. Assume that your current household income is $100,000 per year, and assume that it will grow at the rate of inflation over the foreseeable future. What (constant) percentage of your salary will you have to save each year so that there is enough money to send your child to college? What is the constant amount you will save every year in real dollars, and what are the corresponding (increasing) amounts saved in nominal dollars each year?

Hint 1: For part A, verify your work by calculating the value of the savings account each year and make sure it starts at $0 and ends at $0.

Hint 2: Your answers to parts A and B must be the same in present value terms.

1 I.e., college costs will increase by (1+0.02)*(1+0.03)-1 per year for the foreseeable future.

Answer 1

Part A) The payment amount has to be 5874 each year as shown in the calculations below. (I'm assuming the investments stops in year 16 because end of year 17 (beginning of year 18) college fees start being paid).

Part B) Considering an annual income growing at 2% (inflation rate) starting at 100,000 USD, they need to save 5.16% of annual salary each year to be able to fund the education. Shown below: