ROI Forumla for this scenario

I couldn't come up with a proper formula for the scenario below. I'm not so good at Maths.

With,

$X$ - monthly gains in percentage
$C$ - Initial capital
$N$ - number of years
$M$ - Amount gained (only) after which, gains so far can be re-invested.

I need a formula which can give me the compounded amount for the initial capital X after N no of years

Example: With $3\%$ monthly gains, $M = 30000$ for an initial capital of $10$ Lakh each month would give me $30000$ which equals $M$ , hence the gain of $30K$ can be reinvested next month. Hence gains after second month would be $3\%$ of ($10$ lakh + $30000$).

Let me know if the question is not clear.

To give you some context on why I need this, I m investing in some kind of options(stock derivatives) strategy. I know the average monthly $\%$ gains(expectancy) but the monthly gains can not be reinvested immediately as average cost of a trade is say $30000$. Hence I cannot apply the compound interest formula I believe

Update 1:

I thought about it and created this EXCEL WORKSHEET which I thought might be helpful.

This seems to be the right way to do it. Earlier method was wrong. You will see four images, 1) When transaction cost = 0%, Option not to trade the interest and Option to reinvest are the same. 2) When transaction cost = 3% 3)when transaction cost is .5% and revinvestment rate is 6% and at you described) and finally when the transaction cost is 4% then you will the ROI of the two options in all scenarios. Let me know if this is what you looking for. If you need the worksheet, I shall email it to you.

Good Luck

Thanks

Satish

• Thanks. Please confirm if this correct. Meanwhile, I will also start validating :- As you said, It makes sense logically – chedine Aug 24 '14 at 16:54
• Great, this should do. Looks like it can only be solved using recurrence.. – chedine Aug 25 '14 at 3:57
• You can input the logic in EXCEL using a simple "IF" statement to replace the MAX** component and compute the Future value. I will let you do that. If it is useful, accept the answer and upvote if possible – Satish Ramanathan Aug 25 '14 at 4:16
• Sure, got it and thank you. – chedine Aug 25 '14 at 5:47
• I have made an update and see the solution. I was wrong before and I am hoping that I am right this time if I understand your problem correclty. Thanks for accepting – Satish Ramanathan Aug 25 '14 at 9:26