# Simple investment math

**URL:** <https://boards.straightdope.com/t/simple-investment-math/324676>\
**Category:** Factual Questions\
**Created:** [October 4, 2005, 1:04am UTC](https://boards.straightdope.com/t/simple-investment-math/324676 "2005-10-04T01:04:14Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![CBEscapee](https://avatars.discourse-cdn.com/v4/letter/c/b19c9b/32.png) [@CBEscapee](https://boards.straightdope.com/u/CBEscapee)\
**Post date:** [October 4, 2005, 1:04am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/1 "2005-10-04T01:04:14Z")

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If someone puts $1000 every month for 10 years in an investment account that pays 6% compound interest, how much would they have at the end of the 10 years?

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**Author:** ![Cunctator](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Cunctator](https://boards.straightdope.com/u/Cunctator)\
**Post date:** [October 4, 2005, 1:19am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/2 "2005-10-04T01:19:22Z")

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How is the interest compounded? Does 6% per annum equate to 0.5% compounding per month? If so, then the final amount would be $164,698.74

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**Author:** ![Ringo](https://avatars.discourse-cdn.com/v4/letter/r/779978/32.png) [@Ringo](https://boards.straightdope.com/u/Ringo)\
**Post date:** [October 4, 2005, 1:20am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/3 "2005-10-04T01:20:07Z")

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If it’s compounded annually, I get $167,659.71, or a return on investment of 171.5735%.

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<div class="post-metadata">

**Author:** ![CBEscapee](https://avatars.discourse-cdn.com/v4/letter/c/b19c9b/32.png) [@CBEscapee](https://boards.straightdope.com/u/CBEscapee)\
**Post date:** [October 4, 2005, 1:27am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/4 "2005-10-04T01:27:38Z")

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Ringo, how do you come up with the return on investment of 171%? I’m not good with percentages but out of the $167,000, $120,000 was mine to begin with.

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**Author:** ![Ringo](https://avatars.discourse-cdn.com/v4/letter/r/779978/32.png) [@Ringo](https://boards.straightdope.com/u/Ringo)\
**Post date:** [October 4, 2005, 1:36am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/5 "2005-10-04T01:36:57Z")

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I did the division backwards. Good thing there’s no grade involved. It should be 139.7164%

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<div class="post-metadata">

**Author:** ![CBEscapee](https://avatars.discourse-cdn.com/v4/letter/c/b19c9b/32.png) [@CBEscapee](https://boards.straightdope.com/u/CBEscapee)\
**Post date:** [October 4, 2005, 1:38am UTC](https://boards.straightdope.com/t/simple-investment-math/324676/6 "2005-10-04T01:38:38Z")

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I liked the first rate much better 🙂

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**Author:** ![aamco](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@aamco](https://boards.straightdope.com/u/aamco)\
**Post date:** [October 4, 2005, 7:19pm UTC](https://boards.straightdope.com/t/simple-investment-math/324676/7 "2005-10-04T19:19:35Z")

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A principle P which is invested at a yearly rate of r, interest compounded n times a year for t years, will grow to P\*(1+r/n)[sup]nt[/sup].

So, if you invest some every month, you will end up with a sum of such functions, each with a different time. Let m be the number of subdivisions so that you make m payments of P/m and each payment will have a differing time of -t/m.

P/m\*(1+r/n)[sup]nt[/sup] + P/m\*(1+r/n)[sup]n(t-t/m)[/sup] + P/m\*(1+r/n)[sup]n(t-2t/m)[/sup] + … P/m\*(1+r/n)[sup]n(t-mt/m)[/sup]  
= P/m\*(1+r/n)[sup]nt[/sup]\*(1-(1+r/n)[sup]-n(t+t/m)[/sup])/(1-(1+r/n)[sup]-nt/m[/sup])

P = 120000 (total invested)  
m = 120 (120 payments of $1000 each)  
r = 0.06 (%)  
t = 10 (years)  
n = 12 (monthly compounding)

gives a total of $165,698, or a 38.0% return. If you switch to yearly compounding (n=1), you get $164,124, or a 36.9% return.