Question

Jane Smith wants to send her son Billy to college. Billy just turned 3 years-old today, September

1st, and should enter college on his 18th birthday. After doing some research, Jane finds out that

the tuition cost today for a year of study in a good university in the US is about $50,000 payable

at the beginning of the academic year (September 1st of each academic year). It takes, on average,

4 years to obtain a bachelor’s degree. In addition, college costs typically increase by 5% per year.

How much will Jane have to pay in total for Billy’s college education? In other words, what is the

total amount of dollars that Jane will have paid in tuition costs, once Billy has graduated from

college? Round your final answer to the nearest dollar.

Jane opens a college savings account on Billy’s 3rd birthday, which promises her an effective

annual rate of return (EAR) of 8%. This account, which works like an ordinary annuity, requires

her to invest the same fixed amount at the end of each month, until the beginning of Billy’s last

academic year, when she is expected to make the last of her 4 tuition payments.

What is the monthly periodic interest rate that corresponds to an 8% EAR?

If she makes her first investment in Bill’s college savings account at the end of this month, what

is the fixed dollar amount (round the amount to 2 decimals) that she must invest each month in

order to pay for Billy’s college? (Remember that this savings account requires her to make the

same dollar investment each month, starting from the end of this month until the beginning day,

September 1st, of his last academic year of college.)

Answer 1

Current age of Billy - 3yrs

Entry age in college - 18yrs

Therefore, period of college expense increase = 18 - 3 = 15yrs

Implying that there are 15yrs upto the date on which Billy will enter college

Growth in college costs per year = 5%

Following is the solution on a Financial calculator:

N = Number of years until start of college = 15yrs

I/Y = per year growth in college costs = 5%

PV = Current college costs per year = $50,000

PMT = 0

CPT ---> FV = $103,946

Means Billy's first year college expenses shall be $103,946.41

Assuming the college expenses will grow at the same rate during Billy's college life, the computation of his total college tuition costs will be as follows:

Year	College expense for previous year	Growth rate	College expense for current year	Notes
Year 1			$103,946.41	As computed above
Year 2	$103,946.41	5%	$103,946.41 * 1.05 = $109,143.73
Year 3	$109,143.73	5%	$109,143.73 * 1.05 = $114,600.92
Year 4	$114,600.92	5%	$114,600.92 * 1.05 = $120,330.96
Total			$448,022

Total tuition costs payable by Jane = $448,022

Monthly rate = (1 + EAR)^{1/no. of periods} - 1

Here,

EAR = 8%

No. of periods = 12

Monthly rate = (1 + 0.08/12)^1/12 - 1

= (1 + 0.006667)^1/12 - 1

= (1.006667)^1/12 - 1

= 1.000554 - 1

= 0.000554

Monthly rate = 0.0554%

Monthly periodic interest rate corresponding to 8% EAR is 0.0554%.

Since, the fixed dollar amount is to be invested until start of Billy's final year in college, total number of months will be:

Total number of months = (15 * 12) + (3 * 12) .... 15 years until start of college and 3 years before final year of college

= 180 + 36

= 216 months

On a Financial Calculator:

N = number of months = 216

I/Y = monthly periodic interest rate = 0.0554

PV = current investment = 0

FV = total amount of tuition fees = $448,022

CPT ---> PMT = fixed amount to be saved every month = $1,953.12

Implying that Jane needs to save $1,953.12 per month until start of Billy's final year in college.