Question

A person invested 2,000,000 SR in an account that pays 10% compounded annually.
The first withdraw happens at the end of year 3.
The payments increase at 5% every year until the end of 6th year.
Thereafter, the payments decrease by 5,000 SR every year.
The planning horizon is 15 years.
Calculate the value of the first withdraw such that this investment is attractive (Use PW analysis)

Answer 1

As per the PW or present worth analysis the Future value of the withdrawn from the account should be equal with the value in the account at the end of 3 rd Year.

Let the First Withdrawn is X.

Year	Withdrawl	PVF@10%	Present value of the withdrawn at the end of 3 rd Year
3	X	1	X
4	1.05X	0.9091	0.9546X
5	1.1025X	0.8264	0.9111X
6	1.157625X	0.7513	0.8697X
7	1.157625X-5000	0.6830	0.7907X-3953
8	1.157625X-10000	0.6209	0.7188X-7188
9	1.157625X-15000	0.5645	0.6535X-9802
10	1.157625X-20000	0.5132	0.5941X-11882
11	1.157625X-25000	0.4665	0.5400X-13501
12	1.157625X-30000	0.4241	0.4909X-14728
13	1.157625X-35000	0.3855	0.4463X-15619
14	1.157625X-40000	0.3505	0.4057X-16230
15	1.157625X-45000	0.3186	0.3688X-16597
		Total	8.74X - 109500

Balance in account at the end of 3 Year = 2000000(1.10)^3 = 2662000

Hence 2662000 = 8.74X - 109500

=>X = 317105

Hence the first withdrawl is 317105.

If he withdraws more than the 317105 at the end of 3rd Year then the total present value of the cash withdrawn will be more than the cash available at the account at the end of third year and hence the interest income will be less and the investment will be less attractive.