Question

Investment Plan for Ilkay's Child Education İlkay Yaşam at age of 32 has been working for a worldwide company as an engineer with current net salary 10,000 TL. She decided to make an investment for her child's education for a 10-year time frame. In the last 8 years, she has saved a small fortune as an amount of 50,000 TL. She is little confused about type of the investment that she will make. There are two ways to invest her savings for her child's education. First way is to deposit money for Individual Pension System (IPS). IPS is a system that enables people to carn an income that can maintain their living standards in retirement periods by directing the savings they make during their active working lives to long-term investment. However, although IPS is designed for retirement (more than 10 years), lkay is planning to use the system as 10-year time frame as a saving tool. Second way to save money for her child's education is to create deposit account in a bank for 10-year time frame. Hence, she asked a friend (who took Engineering Economy) for a help that her financial plans by developing the monthly financial plan (cash lows) with taking into account the time value of the money. Bank Deposit: Saving amount of 50,000TL will be deposited in a bank for 10-year period. Estimated MARR values for each year compounded monthly, are given in below table. Note that, the income tax in this type of deposit accounts is 15% for the returns (see below *). |1 2 345 6 7 8 9 10 Estimated MARR (%) 10 11 9 9 85 10 9.5 115 9 8.5 Year IPS System: Her current salary is 10,000 TL. She will save 1,000TL for each month for the first year. For the following years, she will get salary inereases. Her net savings will also be increased as salary increases in same percentages. The 10 year estimated salary increase percentages are given as in below table. 2 3 4 5 6|1 89 10 Increase (%) 3.5 4 3.8 4.1 2.9 34 4.3 2.8 3.7 Year In IPS, she is able to deposit any additional amount at any time. This amount will be withdrawn from bank deposit. Remaining amount will still be kept in the bank deposit. However, she is planning to deposit these extra amount payments anytime between 6" and 10" years. She wants to see from her friend to present at least four different alternative plans that show in which month additional deposit should be made to get maximum accumulated amount at the end of year 10. If she chooses IPS, the govemment provides %25 support in entire accumulated amount at the end. Note that, the annual total government support could not be more than 7,500 TL. But, İlkay will be able to get %60 percent of the govermment support if she quits the system at the end of year 10.

Answer 1

Option 1.Savings bank Account
Year	Interest Rate(%) Compounded Monthly	After tax effective interest rate (Income tax @ 15%) =Interest rate*1-15%	FV of amount invested(A)	Interest Earned FV-Principal Amount
1	10.00	8.50	54,420	4,420
2	11.00	9.35	59,732	5,312
3	9.00	7.65	64,465	4,733
4	9.00	7.65	69,573	5,108
5	8.50	7.23	74,769	5,196
6	10.00	8.50	81,378	6,609
7	9.50	8.08	88,198	6,820
8	11.50	9.78	97,217	9,018
9	9.00	7.65	104,920	7,703
10	8.50	7.23	112,757	7,837
				62,757
				126%
	Annualized Rate of Return = (Current Value / Original Value)(1/Number of Year)			23%
	i.e Rate of return =			23%

Option 2.Individual pension scheme(IPS)
Table showing salary increase and increase in savings in same %
Year	Salary increase %	Salary Amount	Monthly Savings ( 10% of salary)	Total savings for the year
1	-	10,000.00	1,000.00	12,000.00
2	3.50	10,350.00	1,035.00	12,420.00
3	4.00	10,764.00	1,076.40	12,916.80
4	3.80	11,173.03	1,117.30	13,407.64
5	4.10	11,631.13	1,163.11	13,957.35
6	2.90	11,968.43	1,196.84	14,362.11
7	3.40	12,375.36	1,237.54	14,850.43
8	4.30	12,907.50	1,290.75	15,489.00
9	2.80	13,268.91	1,326.89	15,922.69
10	3.70	13,759.86	1,375.99	16,511.83

Year	Rate of return (%) compounded monthly	Total savings for the year	Total Investment (F.V of previous year+ Current year savings)	F.V of total investment	Interest earned
1	11.00	12,000.00	12,000.00	13,388.63	1,388.63
2	10.00	12,420.00	25,808.63	28,511.13	2,702.50
3	8.50	12,916.80	41,427.93	45,089.78	3,661.85
4	9.00	13,407.64	58,497.42	63,984.88	5,487.46
5	10.00	13,957.35	77,942.23	86,103.80	8,161.57
6	9.80	14,362.11	100,465.91	110,766.07	10,300.16
7	10.20	14,850.43	125,616.50	139,045.68	13,429.19
8	12.30	15,489.00	154,534.68	174,651.48	20,116.80
9	12.00	15,922.69	190,574.16	214,743.74	24,169.57
10	11.80	16,511.83	231,255.56	260,069.02	28,813.45
					118,231.18

Option a. Invest for less than 10 year			Governement support @ 25%( limited to 7500)	7,500.00
Total Amount Accumulated				125,731.18
Less: tax @ 10%				12,573.12
Net Income				113,158.06
		Rate of return=		49%
		Annualised Rate of return=		5%

Option b. Invest for 10 year			Governement support @ 60%	70,938.71
Total Amount Accumulated				189,169.88
Less: tax @ 10%				18,916.99
Net Income				170,252.89
		Rate of return=		74%
		Annualised Rate of return=		7%

Advised to invest in Option 1.Savings bank Account which is having high rate of return compared to IPS