Question

1. A senior executive of a public sector company recently quit his job under the VRS with a hefty packet of INR 1 Crore. Ms. Dhana-chor Chit Fund Company has offered the following investment scheme for the benefit of such retired people:

"Invest a certain sum (in lakhs of rupees) in any month; invest half of that amount in the next month. In the subsequent month, one would get twice the amount invested originally in the first month”. This scheme is available only for the next six months (Encashment is possible on 181st day). Returns received at the end of any month can be used immediately for reinvesting either as a fresh investment or as a follow-up investment. Develop a mathematical model to optimize the investment strategy.

1. A senior executive of a public sector company recently quit his job under the VRS with a hefty packet of INR 1 Crore. Ms. Dhana-chor Chit Fund Company has offered the following investment scheme for the benefit of such retired people: "Invest a certain sum (in lakhs of rupees) in any month; invest half of that amount in the next month. In the subsequent month, one would get twice the amount invested originally in the first month”. This scheme is available only for the next six months (Encashment is possible on 181st day). Returns received at the end of any month can be used immediately for reinvesting either as a fresh investment or as a follow-up investment. Develop a mathematical model to optimize the investment strategy.

Answer 1

Answer:

From the given data

Invest a certain sum in any month & invest half of that in the next month. In the subsequent month, one would get twice the amount invested originally in the 1st month

According to above words, Lets invest in

First Month be X1

Second Month be X2

Third Month be X3

Similary, for Money received in First, second & Third Years be Y1, Y2, Y3.

Now,

1==> Invest a certain sum in any month & invest half of that in the next month

From the above line Lets take

X1 + X2 ==> 10,000,000

where from point (1), we understand that

X1 ==> 2 * X2

Then Approximately we get that

First Month (X1) ==> 6,670,000 & Second Month (X2) ==> 3,335,000

Now, Lets take third year

Y3 ==> 2 * (First Month)

Y3 ==> 2*X1 ==> 2 * 6,670,000 ==> 13,340,000

With this we can calculate Third Month

X3 ==> Y3 * (2/3) ==> 13,340,000 * (2/3) ==> 8,893,334

Calculations of the model to optimize the investment strategy:

Month	Investment	Calculations	Output	Calculations
X1	6,670,000	-	-	-
X2	3,335,000	6,670,000/2	-	-
X3	8,893,334	13,340,000(2/3)	13,340,000	6,670,000*2
X4	4,446,667	8,893,334/2	-	-
X5	11,857,779	17,786,668(2/3)	17,786,668	8,893,334*2
X6	5,928,889	11857779/2	-
Final encashment	23,715,558	11,857,779*2

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