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.)