Question

Susan is beginning to plan college savings accounts for her two children. Her son Bobby is 8 and will begin college in 10 years when he turns 18. Her daughter Mallory is 2 and will begin college in 16 years when she is 18. Susan plans to deposit $10,000 per year starting next year into a joint account that earns 8.0% annually. Her last deposit will occur in the year that Bobby starts school. If Bobby’s schooling costs $25,000 each year for four years, and Mallory’s schooling costs $30,000 each year for four years, will Susan’s plan provide enough money for both her children’s college education? By how much will Susan meet/miss the goal when she quits depositing money in year 10? (Assume schooling costs are paid after the year is completed, i.e. Bobby’s first tuition payment will occur at end of year 11)

Answer 1

First let’s make a schedule of savings and expenses of Susan for given time period

After that calculate the future value (FV) of savings at the end of year 10 at discount rate of 8% per annum

Then calculate the Present value (PV) of both her children’s college fees at the end of year 10 at a discount rate of 8% per annum

Year (n)	Savings (S)	Expenses (E )	Future value of saving at 8% interest rate FV = S*(1+8%)^(10-n)	Present value of expenses at 8% interest rate PV = E/(1+8%)^(n-10)
1	$10,000		$19,990.05
2	$10,000		$18,509.30
3	$10,000		$17,138.24
4	$10,000		$15,868.74
5	$10,000		$14,693.28
6	$10,000		$13,604.89
7	$10,000		$12,597.12
8	$10,000		$11,664.00
9	$10,000		$10,800.00
10	$10,000		$10,000.00
11		$25,000		$23,148.15
12		$25,000		$21,433.47
13		$25,000		$19,845.81
14		$25,000		$18,375.75
15
16
17		$30,000		$17,504.71
18		$30,000		$16,208.07
19		$30,000		$15,007.47
20		$30,000		$13,895.80
Total			$144,865.62	$145,419.22
Difference between PV of expenses and FV of savings				$553.60

Susan will miss the goal by $553.60 when she quits depositing money in year 10