So I’ve decided to take a break with the discussion on stocks and investing styles and the like with this post. Instead I’m going to talk about the 8^{th} Wonder of the World (as Einstein famously noted), compound interest.
Compounding occurs when the returns earned one year are re-invested and allowed to grow in future years. For example, say you have $1000 in a ‘high interest’ bank account that pays 1.5% interest. After 1 year, you’ll have $1015 in the account, $1000 of which was your initial investment and $15 of which is your return. Now, if you decide to leave the $1015 in the account for a second year, you would end up with a total of $1030.23 at the end of year two or a total of 23 cents more than if we had withdrawn the $15 at the beginning of the year and spent it. So much for the 8^{th} wonder of the world…
The thing about compounding is that it requires two things to make it effective: time and a decent rate of return. A good rule of thumb to remember is that the doubling time of an investment is approximately 72 / R where R is the compounded annual rate of return. This leads us to the following handy little table relating the rate of return on an investment and its doubling time:
Rate of Return |
Doubling Time |
1.5% |
48 years |
3% |
24 years |
5.5% |
13 years |
8% |
9 years |
9.5% |
7.5 years |
12% |
6 years |
13.5% |
5.3 years |
15% |
4.8 years |
As can be seen, if we keep all of our money in our ‘high’ interest savings account, it will take 48 years for it to double. At that rate of return, the so called savings account may not be working actively against you, but it’s certainly not working for you either.
Now, let’s look at the effects of compounding another way, say we have a 30 year investment horizon and hypothetically $10,000 to invest. At the end of 30 years, how much money are we going to have if we compound our returns at different rates? Let’s take a look:
Rate of Return |
Initial Value |
Value After Year 10 |
Value After Year 20 |
Value After Year 30 |
1.5% |
$10,000 |
$11,605.41 |
$13,468.55 |
$15,630.80 |
3% |
$10,000 |
$13,439.16 |
$18,061.11 |
$24,272.62 |
5.5% |
$10,000 |
$17,081.44 |
$29,177.57 |
$49,839.51 |
8% |
$10,000 |
$21,589.25 |
$46,609.57 |
$100,626.60 |
9.5% |
$10,000 |
$24,782.28 |
$61,416.12 |
$152,203.1 |
12% |
$10,000 |
$31,058.48 |
$96,462.93 |
$299,599.2 |
13.5% |
$10,000 |
$35,477.96 |
$125,868.60 |
$446,555.90 |
15% |
$10,000 |
$40,455.58 |
$163,655.40 |
$662,117.7 |
So, at the end of 30 years, we end up with a total return of 56.3% if we compound at 1.5% per year, or a total return of 6621.8% if we compound at 15% a year. THIS is why compound interest is the 8^{th} wonder of the world.
So practically, what does this mean? It means that as investors, we need to try to maximize both the time we are invested, and the rate of return we receive. Start early and contribute often. Take a look again at the last table. $10,000 can be worth a lot in 30 years time. Or not. It just depends on what you do with it. Which will be the topic of my next post.
Until next time,
Nathan @ EngineeringIncome.com