Question

Please choose one answer A,B,C or D thank you.

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit S2 300 on their daughter's first birthday and plan to increase the size of her deposits by6 each ear. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to: OA. $157,094 OB. S71.407 O c. $142,813 OD. $99,969

Answer 1

The answer is C) $142813

The below table details out the calculations:

Birthday	Deposit Made	Years Remaining Until 18th Birthday	Value of deposit made in the year after compunding until 18th Birthday
0
1	2300.00	17	9953.556844
2	2438.00	16	9679.605738
3	2584.28	15	9413.194571
4	2739.34	14	9154.115821
5	2903.70	13	8902.167679
6	3077.92	12	8657.15389
7	3262.59	11	8418.8836
8	3458.35	10	8187.171207
9	3665.85	9	7961.83622
10	3885.80	8	7742.703113
11	4118.95	7	7529.601192
12	4366.09	6	7322.364462
13	4628.05	5	7120.831495
14	4905.73	4	6924.845307
15	5200.08	3	6734.253235
16	5512.08	2	6548.906815
17	5842.81	1	6368.661674
18	6193.38	0	6193.377407
		SUM	142813.2303

In the table the first column from the left shows the birthday (1 means first birthday, 2 means second and so on).

The second column shows payments made on each of the birthday. The formula used to arrive at the values is :
Previous Payment * (1+rate of increase in size of deposit)
For example, on fourth birthday it will be 2584.28*(1+0.06) = $ 2739.34

The third column represents years until 18th birthday calculated as: 18 - respective birthday
For example, on fourth birthday it is 18-4=14

The fourth column represents the value of the respective year's investment after it has grown because of compounding until 18th birthday.
This is calculated as: Value in second column for respective year * (1+rate of compounding)ⁿ where n is the value in third column.
For example, for fourth year it is : 2739.34 * (1+0.09)¹⁴ = 2739.34*1.09¹⁴ = $9154.12

To arrive at total accumulated value on the 18th birthday, all the values in the fourth column as calculated above are added up.

Thus, $142813 is the answer.