Question

Please, be neat and detailed. Explanations would be great. I need to understand it. Thank you.

Question 122 points total). Your sister is starting to plan for your niece's college expenses and has asked for your advice. Elle has turned 6 years old today and she will start college when she is 18 years of age. Your sister plans to start saving today, by making a deposit of $5,000 into an account that earns 6% interest per year. Then, she will continue to make deposits at the end of each of the next 12 years, increasing the amount of the deposit each year by $1,500 (a) [12 points) How much will your sister have saved by the time Elle is 18 years of age (ie, at the end of the 12 year). U tiron Perooo (b) [10 points while your sister is uncertain about how much Elle's education will actually cost, she does anticipate that college costs will increase by 2.5% each year over the previous year's cost. Elle will make the first withdrawal to pay her expenses at the end of her 19 year of life i.e. at the end of the 13 year), and will continue to make an end of the year withdrawal for five total years in which she is a student (year 13 through 17). Ultimately, your sister's goal is that the deposits that she will make will match exactly the expenses that Elle will have during college. If this is true, how much can Elle's first year of college cost? The interest rate for the withdrawal period remains the same as the deposit period.

Answer 1

Age	Year	Deposits	FV
6	0	5,000.00	10,060.98	=5000*(1.06)^12
7	1	6,500.00	12,338.94	=6500*(1.06)^11
8	2	8,000.00	14,326.78
9	3	9,500.00	16,050.05
10	4	11,000.00	17,532.33
11	5	12,500.00	18,795.38
12	6	14,000.00	19,859.27
13	7	15,500.00	20,742.50
14	8	17,000.00	21,462.11
15	9	18,500.00	22,033.80
16	10	20,000.00	22,472.00
17	11	21,500.00	22,790.00
18	12	23,000.00	23,000.00	=23000*(1.06)^0
		Total	241,464.13

Initially the amount will be invested for 12 years, then 11 years, then 10 years and will therefore each subsequent deposit will be calculated as per the table given above.

The formula to calculate the withdrawals is PMT(0.06,5,241,464.13) = -57322.72
This can be shown as per the schedule below:
Initial end deposit = 241,464.13*1.06
End deposits = End balance*1.06

Age	Year	End Deposits	Withdrawals	End balance
19	13	255,951.98	-57,322.72	198,629.26
20	14	210,547.02	-57,322.72	153,224.30
21	15	162,417.76	-57,322.72	105,095.05
22	16	111,400.75	-57,322.72	54,078.03
23	17	57,322.72	-57,322.72	0.00