Question

cation fund for your child. The current cost for college 7 You plan to establish a college education fund for your child. The 000 per vear and you expect this cost to increase by $600 per year. You plan to deposit money into an account earning 10% yearly nominal interest, compounde monthly, at the end of each year for the next 17 years. You will withdraw the ar required for college in the end of years 18 to 21 to pay for college for years 18 to 21. respectively. You would like to deposit a low initial amount, which you plan to increase at a rate of $50 per year. How much is your first deposit (end of year 1) to this account? HINT: Equate the present value of the cost of college to the present value of your savings.

Answer 1

End of year	College Fee	Remark
1	12,000
2	12,600
3	13,200
4	13,800
5	14,400
6	15,000
7	15,600
8	16,200
9	16,800
10	17,400
11	18,000
12	18,600
13	19,200
14	19,800
15	20,400
16	21,000
17	21,600
18	22,200	College Fee Required
19	22,800	College Fee Required
20	23,400	College Fee Required
21	24,000	College Fee Required

Effective Annual Interest Rate :  

[(1+r/n)^n]-1 where r = rate of Interest , n = Compounding in a year

[(1+0.10/12)^12]-1

=[(1+0.00833)^12] -1 = 0.10471 or   10.471%

Year	Amount to be paid	PV factor @10.471%		Present Value
18	22,200	1/1.10471	0.90521	20,096
19	22,800	1/1.10471^2	0.81941	18,683
20	23,400	1/1.10471^3	0.74175	17,357
21	24,000	1/1.10471^4	0.67144	16,115
Present Value at the end of 17th Year				72,250

Deposit	Opening	Deposit Amount	Cumulative Amount for Interest	Interest Effective	Withdrawn	Closing
1	-	1,258	1,258	132	-	1,390
2	1,390	1,308	2,698	283	-	2,981
3	2,981	1,358	4,339	454	-	4,793
4	4,793	1,408	6,201	649	-	6,851
5	6,851	1,458	8,309	870	-	9,179
6	9,179	1,508	10,687	1,119	-	11,806
7	11,806	1,558	13,364	1,399	-	14,763
8	14,763	1,608	16,372	1,714	-	18,086
9	18,086	1,658	19,744	2,067	-	21,812
10	21,812	1,708	23,520	2,463	-	25,982
11	25,982	1,758	27,741	2,905	-	30,645
12	30,645	1,808	32,453	3,398	-	35,852
13	35,852	1,858	37,710	3,949	-	41,658
14	41,658	1,908	43,567	4,562	-	48,128
15	48,128	1,958	50,087	5,245	-	55,331
16	55,331	2,008	57,339	6,004	-	63,343
17	63,343	2,058	65,402	6,848	-	72,250
18	72,250	-	72,250	7,565	22,200	57,615
19	57,615	-	57,615	6,033	22,800	40,848
20	40,848	-	40,848	4,277	23,400	21,725
21	21,725	-	21,725	2,275	24,000	-0

So First Deposit Amount will be $1258