My Math Forum Calculating Return

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 September 17th, 2008, 12:05 PM #1 Newbie   Joined: Aug 2008 Posts: 6 Thanks: 0 Calculating Return With an investment of $2000, can anyone show me how to calculate what rate of return I need to provide a dividend of$200/week? (if possible)
 September 17th, 2008, 02:25 PM #2 Member   Joined: Aug 2007 Posts: 93 Thanks: 0 Re: Calculating Return It all depends, how much you step on the dope? do you have to pay protection? How many corners do you control?
 September 17th, 2008, 02:32 PM #3 Newbie   Joined: Aug 2008 Posts: 6 Thanks: 0 Re: Calculating Return Thanks for that. However, I was looking for a mathematical reponse. And yes, I know it depends on the circumstances, but I was hoping for a reponse that would illustrate how this could be achieved mathematically, in a range of circumstances.
 September 17th, 2008, 02:54 PM #4 Member   Joined: Aug 2007 Posts: 93 Thanks: 0 Re: Calculating Return Do you actually have plans to find an investment that pays a 420% (52*200 / 2000) annualized rate of return?
 September 17th, 2008, 03:46 PM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Calculating Return A continuous rate of return gives return = exp(r * t), so you're trying to solve $200/$2000 + 1 = exp(r / 52) 1.1 = exp(r / 52) r / 52 = log (1.1) r = 52 log 1.1, which is 496%. STV did the simple interest case already (though he figured on running out of money after the phenomenal first year; if you figured on having the $2000 in addition to the monthly earnings, that would be 620%).  September 17th, 2008, 04:11 PM #6 Member Joined: Aug 2007 Posts: 93 Thanks: 0 Re: Calculating Return Well if you reinvested the income the investment would surpass the value of total US GDP in about 5 years I am just trying to be conservative here September 17th, 2008, 04:50 PM #7 Newbie Joined: Aug 2008 Posts: 6 Thanks: 0 Re: Calculating Return Quote:  Originally Posted by STV Do you actually have plans to find an investment that pays a 420% (52*200 / 2000) annualized rate of return? No. This is a mathematical exercise to help me understand how to calculate the interest rate I would need to achieve this objective. It is also to help me understand how to calculate the investment capital required to generate a specific return on my investment. September 17th, 2008, 04:54 PM #8 Newbie Joined: Aug 2008 Posts: 6 Thanks: 0 Re: Calculating Return Quote:  Originally Posted by CRGreathouse A continuous rate of return gives return = exp(r * t), so you're trying to solve$200/$2000 + 1 = exp(r / 52) 1.1 = exp(r / 52) r / 52 = log (1.1) r = 52 log 1.1, which is 496%. STV did the simple interest case already (though he figured on running out of money after the phenomenal first year; if you figured on having the$2000 in addition to the monthly earnings, that would be 620%).
Thanks for your help. It is much appreciated. Can you show me how you calculated a return of 620%?

September 17th, 2008, 05:05 PM   #9
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Re: Calculating Return

Quote:
 Originally Posted by damo12 Thanks for your help. It is much appreciated. Can you show me how you calculated a return of 620%?
Just like STV did, but with $2000 added to the$200 * 52.

September 17th, 2008, 06:14 PM   #10
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Re: Calculating Return

Quote:
Originally Posted by CRGreathouse
Quote:
 Originally Posted by damo12 Thanks for your help. It is much appreciated. Can you show me how you calculated a return of 620%?
Just like STV did, but with $2000 added to the$200 * 52.
Its 520% with the return of the \$2000

But the point is that there are a number of methods to calculate a percentage return. In practice continuous returns only get used in academic finance, in the investment business it is discrete compounding.

Your investment makes 10% a month, as CR & my calculations show it makes a big difference whether or not you reinvest and compound the income. The difference is less of course at more realistic rates of return.

The general discrete formula is V(t+1) / V(t) -1 (V(t) = value at time t). If you want to compound n individual periods it is [V(t+1) / V(t)]^n -1. If you want to take a cumulative return over n periods and calculate the n-uallized return it its [V(tn) / V(t)]^(1/n)-1

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