# Profit maximization equation

rani0712
Hey guys

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Hope i can contribute tooo!

If a Share costs 3 dollars, and it doubles every 3 months
And nother share costs 1 dollar and doubles in One month

How many shares of each would you buy with 1000 dollars, to gain the most profits in 6 months>?

Homework Helper
If you invest x dollars in the first, it would be worth $(x/3)2^{n/4}$ dollars in n years. If you invest x dollars in the second it would be worth [itex]x(2^{n/12}}[itex].
The ratio of those is
$$\frac{1}{3}2^{n/4-n/12}= \frac{1}{3}2^{n/6}$$
For N= 6, that ratio is 2/3< 1. What does that tell you?

DKATyler
Latex Image generator doesn't appear to be working so:

The first gives an annual ROI of:
(3*212/3)/3

The second gives an annual ROI of:
(1*212/1)/1

You want the maxmimum amount of shares of the one that gives the largest ROI for 6months.