Joe and June Green are planning for their children\'s college education. Joe wou

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. (a) 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? (b) Joe is worried that he and June cannot afford to contribute to the college fund right away. He suggests waiting a few years before making the equal annual contributions. If Joe and June begin making deposits on August 31, 2019, rather than August 31, 2016, how much higher with their annual deposits have to be? (c) If the mutual fund earns 7.8% compounded quarterly, will the amount required in part (a) be higher or lower? Support your answer.

Explanation / Answer

a) Amount to be deposited in the college fund each year = $4,484 Calculations: 18th year 19th year 20th year 21st year beginning beginning beginning beginning Tuition fee 37460 38958 40516 42137 Pvif(8,0-3) 1.0000 0.9259 0.8573 0.7938 PV at the beginning of the 18th year 37460 36072 34736 33450 Total amount to be had in the fund ` at the beginning of the 18th year (sum of the PVs of the tution fee) 141718 This amount of $141718, should be the FV of the lump sum of $5000 deposited on the day David was born + the FV of the annuity that his parents are goind to deposit every 31st August. So, 141718 = 5000*fvif(8,18) + A*fvifa(8,15) assuming that no deposit would be made in the year in which David joins college. 141718 = 5000*3.9960 + A* 27.1521 (141718-19980)/27.1521 = A = $4,484 b) The equation becomes 141718 = 5000*fvif(8,18) + A*fvifa(8,12) 141718 = 5000*3.9960 + A* 18.9771 (141718-19980)/18.9771 = A = $6415 The amount to be deposited yearly would become $6415 c) If the MF earns 7.8% compounded quarterly the effective rate of interest would become EAR = (1+0.078/4)^4 - 1 = 0.0803113 = 8.03% As the EAR is marginally more than the annual rate of 8%, the annual amount to be paid would be less. Check: 141718 = 5000*4.0160 + A* 27.2156 (141718-20080)/27.2156 = A = $4469 The annual deposit required decreases by $15.

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.