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If I have increasing debt that I don't intent to pay off for a really long time, how would I prefer to have it grow?

Exponentially, logarithmically, or linearly?

Will Martin
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    You would prefer a logarithmic growth of course, since it's the slowest. However, I doubt you would ever find a creditor to offer you such a loan – Yuriy S Mar 14 '16 at 08:46
  • That question doesn't make much sense. The growth rate doesn't tell you anything about the amount you have to pay off. Also, a logarithmic function has an unavoidable negative tail to infinity. –  Mar 14 '16 at 09:34
  • This is perhaps silly. But I too often hear "logarithmic growth" used synonymously with "exponential growth". – Will Martin Mar 14 '16 at 09:40
  • @YuriyS yeah I doubt that too. Perhaps one could convince parents to give a logarithmic loan with an initial interest rate 10%. – Will Martin Mar 14 '16 at 09:44

2 Answers2

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As Yuriy S says, you should choose the logarithmic, since it will (eventually) be overtaken by the two others no matter how you tweak the parameters. The exponential function is by far the fastest growing of the three, and it is sadly also the one most (all) loans use. See this question about comparing growth rates.

Here are the three functions plotted, with all parameters set to $1$ (note that the differences only become more clear the bigger $x$ becomes):

enter image description here

Community
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Bobson Dugnutt
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Exponentially, the fastest growing way, so that you pay the most in the end.

enter image description here

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    Isn't the graph in fact a great illustration that asymptotic results are not to be mindlessly used in finite horizon setting? – A.S. Mar 14 '16 at 09:34
  • @A.S. I didn't think of it this way, but yes. –  Mar 14 '16 at 09:35