Question

This problem is similar in spirit to Example 12 (in the chapter) and Problem 15 (at the end of the chapter). I'd strongly suggest that you master those two problems before attempting this problem. Make sure that you draw a high quality, detailed timeline – similar in quality to those in Example 12 and Problem 15. Assume that you wish to begin saving for your child’s college education via making deposits into an investment account that is expected to earn 8% per year for the first 14 years. After year 14, you will place the money in a less risky investment account that is expected to earn only 5% per year, for as long as you have money in the account. You currently have $5,000 available, and you will deposit that amount into the savings account today. Thereafter you have decided to make savings deposits 3, 4, 5, … , 9 and 10 years from today. Each of these deposits will be larger than the prior deposit by 7%. You’ve estimated that one year of college will cost $52,000 in 18 years, and that the three subsequent years will each cost 5% more than the prior year. Determine the size of the first deposit required at time 3.

Answer 1

So I created a Excel sheet, with Opening balance, payments, interest earned as per interest rates mentioned and closing balance etc to come up with how much payment is needed in Year 3 and subsequent years till year 10 to be able to have enough money to pay for college in years 18,19,20 and 21 totaling up to $224,127.

The payment needed in year 3 is 7769. Calculations as below.