Comments on: A Visual Guide to Simple, Compound and Continuous Interest Rates http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Fri, 6 Nov 2009 22:26:19 -0800 http://wordpress.org/?v=2.8.4 hourly 1 By: Kalid http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-226573 Kalid Wed, 18 Feb 2009 22:07:38 +0000 http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-226573 @George: Hi, e is the result of 100%, continuously compounded interest. You can try the article on e (see first paragraph) for more details. @George: Hi, e is the result of 100%, continuously compounded interest. You can try the article on e (see first paragraph) for more details.

]]> By: George http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-219163 George Fri, 26 Dec 2008 19:03:36 +0000 http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-219163 I have this question: How does 'e' relate to compound interest? Happy holidays! I have this question:

How does ‘e’ relate to compound interest?

Happy holidays!

]]> By: Kalid http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-211127 Kalid Thu, 23 Oct 2008 00:16:36 +0000 http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/#comment-211127 @Armin: Glad you enjoyed it, those are great questions. 1) This is where the natural log comes into play. If you want a "final" return of 50% (that is, 1.00 becomes 1.50) you can do ln(1.50) = .405. That means an interest rate of 40.5% will get you 50% return if it's compounded as fast as possible. So, 40.5% is the "safe" rate you can use. If you know you'll only compound twice, then you can solve the equation: (1 + r)^2 = 1.5 (1 + r) = sqrt(1.5) [take square root] r = sqrt(1.5) - 1 [subtract 1] r ~ .22 So, if you only compound twice (halfway & end of year) then you are safe with a rate of 22%. 2) That's a really good question. The formula is a bit more complicated because you have to account for each deposit, which come in at different times. There's more info here: http://www.maths.leeds.ac.uk/Applied/0380/savings04.pdf I think that would make a good follow-up article, as a similar formula is used to calculate loan payments (you pay the same amount each month for the loan, but how to do they work out that number given the interest?). @Armin: Glad you enjoyed it, those are great questions.

1) This is where the natural log comes into play. If you want a “final” return of 50% (that is, 1.00 becomes 1.50) you can do ln(1.50) = .405.

That means an interest rate of 40.5% will get you 50% return if it’s compounded as fast as possible. So, 40.5% is the “safe” rate you can use.

If you know you’ll only compound twice, then you can solve the equation:

(1 + r)^2 = 1.5
(1 + r) = sqrt(1.5) [take square root]
r = sqrt(1.5) – 1 [subtract 1]
r ~ .22

So, if you only compound twice (halfway & end of year) then you are safe with a rate of 22%.

2) That’s a really good question. The formula is a bit more complicated because you have to account for each deposit, which come in at different times. There’s more info here:

http://www.maths.leeds.ac.uk/Applied/0380/savings04.pdf

I think that would make a good follow-up article, as a similar formula is used to calculate loan payments (you pay the same amount each month for the loan, but how to do they work out that number given the interest?).

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