Question

Joe and June Green are planning for their children's college education. Joe would like his kids to attend his alma mater where tuition is currently $20,000 per year. Tuition costs are expected to increase by 4% each year. Their son, David, just turned 2 years old today, September 1, 2015. David is expected to begin college the year in which he turns 18 years old and each will complete his schooling in four years. College tuition must be paid at the beginning of each school year on August 31.

Grandma Green invested $5,000 in a mutual fund the day David was born. The mutual fund investment has earned and is expected to continue to earn 8% per year. Joe and June will now begin adding to this fund every August 31st (beginning with August 31, 2016) to ensure that there is enough money to send David to college.

How much money must Joe and June put into the college fund each of the next 15 years if their goal is to have enough money in the investment account by the time David begins college?

Answer 1

Joe and June need to calculate annual payments combining future value of annuity and compound interest formulas to meet the expected tuition costs at Joe's alma mater for David's college education considering tuition increases and investment growth.

Step-by-step explanation:

Joe and June need to make annual payments into a college fund that will grow to meet the rising tuition costs by the time their son, David, goes to college. The tuition for Joe's alma mater is currently $20,000 and is expected to increase by 4% annually. To compute the required annual payment, we will use the future value of an annuity formula for the payments and the compound interest formula for the initial $5,000 investment.

To solve this calculation, we need to determine the future value of the $5,000 at an 8% interest rate over 16 years, the future value of the annuity that represents the annual payments at 8% over 15 years, and the present value of the tuition costs, increasing at 4% annually over four years starting from the 16th year.

This problem assumes continuous growth and does not account for variability or risk, such as the investment earning a different return or tuition increases fluctuating. Such assumptions are typical in financial planning to provide an estimate of the savings needed.