Question

*assume the child will be in college for four years*

(A) It is estimated that 18 years from now college tuition will be $42,000 per year. If your child was born today, how much will you need to put away per year, at the end of each year through your child's 18th birthday, so that no additional payments need to be made after year 18? Assume i = 3%

(B) Assume the same parameters as A, but now assume that after year 18, tuition will increase $1,500 per year.

(C) Check your answer to B above by computing the same figure using a different method.

Answer 1

A) It is case of compound interest.

Here total period (n) = 18 years, rate of interest (i) = 3% therefore, r = i/100 = 3/100 = 0.03

Amount (A) = $42,000*4= 168000 (Since the period of study is 4 years and tution fee is $42,000 per year)

Therefore, principal amount(P)= A/(1+r)ⁿ = 168000/(1+.03)¹⁸ = 98682.29 Also total interest after 18 years= A-P = 168000-98682.29= $69317.71.

Therefore, the money amount that you need to pay each year for your child's education is average of the sum of principal and total interest = (98682.29 +69317.71)/18= $9333.333.

B) If the tution fee is expected to increase by $1500 per year then total increase in tution fee for 4 years is = $1500*4 = $6000

Therefore, the total amount that you will need for your child's tution after your child's 18th birthday = $42000 *4+$6000= $174000

Therefore P =174000/(1+0.03)¹⁸ = $102206.66

Also total interest in 18 years = A-P=174000-102206.66=$71793.34

therefore, you need to put away amount which is equal to average of principal amount and total interest = (102206.66+71793.34)/18= $9666.666.

C) Using annuity table for discrete compounding we found the value of amount factor

(F/A,3,18)= 18.388

Therefore, the minimum amount that you need away each year for your child's education = Amount(A)/Amount factor value = 174000/18.388= $9462.69 which is near to value shown in (B).