A Visual Guide to Simple, Compound and Continuous Interest Rates

Interest rates are confusing, despite their ubiquity. This post takes an in-depth look at why interest rates behave as they do.

This is a companion discussion topic for the original entry at http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/

Your articles are excellent, I just wait for the new ones to arrive and as I soon a new one appears, I am all excited to read.

Please keep going, thanks for all the better explanations.


Just a quick comment, I love your site and your articles… But here’s something I noticed…

When you’re stating “return = (1 + r/t)^tn” you need to make sure that you put the Principle in there :).

Return = P(1+r/t)^tn

This had me hammered for a little while as I tried to work out where we put the principle.

Admittedly I may just have been slow… :wink:

@Srikanth: Appreciate the comment! Glad you’re finding the articles useful.

@Zachary: Thanks, that’s a good catch – just fixed it :). Nope, you’re right, it’s important to get those types of details correct.

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Dear Sir:

In the same breath, can you explain how scientists arrive at half life of radio-active material.



another fun one! I love the way you simplify concepts without being condescending. Also, you leave ‘room’ for me to go off and find out more now that I have the basics down (basics with a different insight). The idea of ‘interest’ comes everywhere. For example, if you were in charge of cash flow at a factory. The ‘interest’ could be considered the ROI (return on investment) of the widget. If you had one dollar (it is a small factory) would you be better off paying the factory bills which amount to $1 or buying raw materials for the factory. Well let’s say you could buy materials for $1 and produce a gaggle of widgets which you can sell in the prescribed period of say 14 days. You can get payment in (I know lots of assumptions) in 25 days AND the bills are not due till net 30. Now the profits of that principal is $3. Cash flow being a function of interest aka time… did this have anything to do w/ your article???

[…] A Visual Guide to Simple, Compound and Continuous Interest Rates | BetterExplained (tags: finance money interest howto reference **mathematics) […]

Thanks Mr. Rose! Yes, that’s an interesting application – if you have the choice between paying bills later (in 30 days) or investing in your business today, the investment is a good idea because it will give you more breathing room down the road. And then you can reinvest those profits to become even more profitable.

@T.Gopalan: Hi, good question. Radioactive half-life is a bit different: rather than giving an interest rate, it’s more like an interest “time” – i.e., how long does it take for a material to decay to half it’s value?

This would be like giving interest rates in terms of the time needed to double: rather than 10% interest, you’d say “I have a doubling rate of 7.2 years” (or “halving rate” if your material is decaying by 10%/year).

I imagine expressing half life this way is useful because you often want to know the time, for figuring out things like carbon dating. In another article I’ll discuss how to convert from one to the other, but check out the Rule of 72 for more info.

Great article. APR versus APY is a distinction I’ve forgotten repeatedly, this should help it stick much better…

Thanks, glad you liked it! Yeah, I wish someone had told me earlier that APY is the rate you usually care about (“price after tax, shipping and handling”).

Kalid - again, I’m so impressed! I can’t tell you the number of times I’ve looked at interest rates and had no clue what it really meant. The way you structured the article was also very helpful to understanding the main points. I did notice the many e plugs, so I guess I’ll try to tackle a concept that has evaded me since high school. thanks!!

Nice article, Kalid. I think a more theoretical article would be useful too – one that discussed why interest rates exist at all and how they relate time and money.

Hi Jonah, thanks for dropping by. I agree, I think that’d be a great follow-up article, appreciate the suggestion.

@Desi: Awesome, so glad you liked it :slight_smile:

This is just brilliant. I have never quite understood e but this is so soooo simple. Even an old fella like me can learn something. This is a style of teaching that should be compulsory in all areas. Talk to me not at me and get results. Thanks heaps.

You’re welcome Stephen, I’m glad you enjoyed it. Rest assured, there’s plenty of young fellas (myself included) who went through the motions of e without really understanding what it was about :).

Hi Kalid,
This and the other articles on this site are really amazing!

It really explains concepts better than what they do in schools!

Take care and God bless!

Thanks, glad you’re enjoying the site! :).

Hi Kalid! This article is excellent!! I really enjoy your slogan philosophy: “Learn right, not rote.” Too often I think we’re shortchanged with understanding…

Just a quick catch of my eye:

(1) In your “Compound Interest” graph (the one that’s all blue), I believe the last column should be $337.50 not $327.50.

(2) If you do a quick find for the text “For a 1 year, the impact of rate r compounded t times is:”, I believe the “a” should be removed.

Your website is an inspiration and I look forward to learning more form you!

Thanks so much! :slight_smile: