## Compound Interest Week: An Introduction |
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A lot of personal finance bloggers write about compound interest. I have written about it myself in the past. This week, I'd like to cover compound interest in more detail than I have in the past. I hope to cover some new ground in this area and/or put a little twist on the topic.

I think I've always had a slightly more pessimistic, but probably more realistic view of how it really works. We'll get into an example first, but here's a handy chart that we'll refer to time and again... Thanks to Golbguru of Money, Matter, and More Musings for providing the chart on the left as well as this quote on compound interest:

"Another quick and crude way to estimate the time is to 'double rate and half time'- meaning, if you double your rate of return (interest rate), it will take half as much time to double your money. For example, at 1% interest rate it takes about 70 years to double your initial investment, so at twice the interest rate (2%) it will take about 70/2 = 35 years; and if you double it once more (4%) it will take about 35/2 = 17.5 years.... A rise of rate of return from 1% to 4% (a difference of 3%) has a drastic effect on reducing the time (from about 70 years to about 17.5 years), however, a rise from 17% to 20% (again a difference of 3%) reduces the time from 4 years and 5 months to just 3 years and 10 months."

I have to agree that going from 1-4% is a huge difference. If I'm making just 1% my money is going to double just once in my lifetime, if I'm lucky. If I'm making 4%, my money may double 3-4 times in my life. So if I start with $1000, at 1%, in 70 years I'll end up with $2000. However, at 4%, I'll end up with $16,000 as the original $1000 becomes $2000 after 17.5 years, $4000 after 35 years, $8000 after 52.5 years, and $16,000 after 70 years. That's very significant indeed.

Let's take the 17% to 20% and see how that works over 70 years. The math is may get a little difficult, but I'll walk you through it. First off, instead of dealing with years we'll convert everything into days. It's simply an easier unit to work with - rather than saying money at 17% doubles in 4.1666 years, we can say it doubles in 1612 days (give or take a leap year). If you are able to earn a 17% gain, according to the chart your money does indeed double every 1612 days. In the 70 year (25550 days) outlook that we were using above, that means that it will double 15.85 times in that span. A 20% compound interest rate will double every 1400 days or a total of 18.25 times in a 70 year time span. How much is the $1,000 worth? Hold onto your hats - a little over 59 million dollars. At the 20% interest rate, $1000 becomes a jaw-dropping 311.7 Million dollars. I'd be okay with either number, but the difference between 17% and 20% is indeed a lot bigger than it looks when it's applied to standard lifetime.

That sad thing is that it's nearly impossible to earn either 17% or 20% on average for a span of 70 years. However, this illustrates what a great difference one percentage point of interest can be over a long span. We'll come back and build on this later in the week.

(Thanks to Money, Matter, and More Musings for the chart.)

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Next: Compound Interest Week: The Real Rate of Return

One GUARANTEED way to make 17% per year is to start up a credit card company!

Its not so easy to have a CC company. you have to deal with defaults. You have to deal with giving people free loans for 30 days. You also have to have rewards to get many people to get the card.

No way does that come out to 17%

Instead of saying “it will take half as much time to double your money”, why not say that you will have a huge amount more in the same time. Take the below chart: notice that doubling the rate over, say 15 years, produces 3 times the return (you have $4.2 for every dollar instead of $2.1). After 25 years your returns are almost 5 times.

Years 5% 10%

1 1.05 1.10

5 1.28 1.61

10 1.63 2.59

15 2.08 4.18

20 2.65 6.73

25 3.39 10.83

30 4.32 17.45

In compound interest the sensitivity is with time and interest rate. The initial investment almost doesn’t matter, just invest something, anything, to get the benefits.

Customer’s Revenge, I usually do it that way, but I liked the simplicity of time to double your money for this example. Telling people that they can double their money in 70 years, I think is a sobering thought vs. 7 years.

Of course we also aren’t counting some things like inflation and taxes at this stage… That’s later this week.

The sad part is that taxes are a killer, they can pull the rug right out from under the power of compounding.

The math isn’t hard, but in general, if the rate is low: seventy divided by the rate (for a number of periods) will give you the doubling time (in terms of those periods) to a very close approximation. In an inflation ridden country – 70 divided by inflation rate will give you, close enough, the number of periods in which you will have to be earning twice what you are earning now: If inflation is double digit, at say 15% per year – you’d have to earn double in 70/15 = 4.7 years. A day trader that can work an average gain of 3% per day – with no failures (pretty sharp!) would double his capital in 70/3 = 23 working days, or a little more than a month…

The method is used in nuclear physics, to estimate the “half life” of a radioactive isotope: a gramme of Carbon 14 would be 1/2 gramme in 5570 years (which makes it useful for dating ‘historical’ times); a gramme of Plutonium 239 would be down to half that in some 20 000 years, which is why we don’t want the stuff around (of course, its quicker decay, as in a fission blast we don’t want at all)

An alternative to starting a credit card company is supplying loans to borrowers at prosper. With a diversified portfolio, you can earn 15 to 17% easily. I only have about $100 invested, but I plan to increase that amount in the next couple of months. Besides, spending the time finding trustworthy borrowers is invaluable. Then once you calculate compound interest gains over say the 3 year loan period, you will be amazed at all the money Visa and American Express earns. It’s truly powerful!

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[…] The pretax portion of the SEP-IRA is what makes it so attractive to non 401K users. By deferring taxes you not only save in cash flow today, but push out the dollar cost of your eventual taxes so that their NPV is significantly less even if you are in a higher tax bracket in retirement. And on top of that you get the value of compounding interest. […]

Lazy man, good job with explaining compound interest in a different way. Sometimes, it’s better to read articles with different views from different authors about one topic to get a better grip of the concept. I read your article some time ago and caught myself using your explanation when explaining compound interest to a friend. Thanks!