The World Needs More Ninjas

Say I want to drive to Chicago, which is a couple of hours away, and I need to be there by noon. There are a couple of considerations I must take into account if I want to reach this deadline. First, what time will I leave Champaign and, second, how fast can I go (i.e., at what rate). The upper bound on the second factor, the rate, is somewhat fixed by factors such as traffic, wrecks, state troopers, and how fast the car can go. I’m probably not going to be able to average more than 80 mph for the trip. If I leave at 11:30 am, I’m pretty much screwed because it’s physically impossible to achieve a high enough rate to make it to Chicago by noon.

By contrast, I do have much more control over the first factor, what time I leave. Obviously, there are some constraints on this such as if I have meetings in Champaign that morning, but, generally speaking, I have much more flexibility to control the departure time in order to reach my goal.

Investing for retirement is similar. You don’t have much control of the rate of interest on your investments. You generally can’t sustain an average annual rate of more than 10% over a long period (short term you can, but the risk gets to the point where it will bite you in the long run). The deadline is how much money you want to have saved by the time you retire (or at some other point during your life, such as when your kids go to college).

Say that you’re currently 25 years old and you want to have $3.7 million by the time you are 70 years old (this would correspond to roughly $1 million in today’s dollar value). If you start saving at 25 and get an annualized return of 8%, you’d need to save about $8400/year to reach your goal. Thus, that 45 year period, you would save only $378000, but end up with ten times as much money in your bank account! Sounds pretty good.

But, if you waited until you’re 50 to start saving, you’d have to save $46000/year to reach your goal. This means that over that 25 year period, you would save a total of $1.15 million and only end up with about 3 times as much money in your bank account. Thus, you can see that time is a much more important factor than rate when it comes to reaching your goal.

The reason is, of course, due to the magic of compound interest. Any time you mention the phrase, you’re obliged to include the Einstein quote: “The most powerful force in the universe is compound interest”. If you put $100 in the bank and get a 10% return, then after a year, you’ll have $110. As first glance, you might expect to have $120 after year two. However, since you’re earning interest on your interest, you’d actually end up with $121. That extra dollar isn’t that big of a deal in the short term. But, when you keep doing this over the period of decades, you get exponential increase. The math formula to demonstrate this is:

Where FV is the future value, PV is the present value, i is the annualized interest rate, and n is the number of compounding periods (e.g., years). So, the future value is exponential with the number of years.

If you continue to add money every year, as I was discussing earlier, you end up with the following equation:

Where r is the annualized interest rate and payment amount is how much you put in each compounding period.

Another little interesting trick is the Rule of 72 that helps you calculate the effects on compound interest more easily. It says that if your annualized rate is r, then your principal amount will double approximately every 72/r years. So, if you get a 10% rate of return, your principal will double about every 7.2 years. Similarly, if the rate of inflation is historically 3%, then the price of items will double about every 24 years. So, for most of us, we’ll see prices double 3-4 times in our lifetimes. That means that by the time you die, things will cost 8-16 times as much as they did when you were born.

OK, so what’s the moral of this post? That you should start saving for retirement first thing tomorrow if you haven’t already. If you have started, make sure you do it regularly and don’t skimp. Your teens or twenties doesn’t seem like the optimal time to start saving since you probably have hardly any money if you’re lucky or else you’re neck deep in debt from student loans, car payments, and mortgages. But, committing yourself now will help you exponentially in the future.

Just as an illustration of what a little change in your spending can do, say that you spend $20/week on something that you don’t really need. Maybe it’s eating out an extra time or buying something that you don’t really need that you’ll be giving to Goodwill in a year anyway. That money comes out to $1040/year and, if saved at 8% for 45 years, would end up being worth $460000!

And, if empirical evidence is any indication, it’s likely you’ll never have enough money to start saving unless you explicitly commit to it. Once the student loans are paid off, you’ll be saving for your kids’ college. Once the car is paid off, you’ll have maintenance or a new car payment to start. That mortgage will more than likely be with you for 30 years. So, given that you’re going to be stretched thin your whole life, you might as well start saving now when your money is worth significantly more than it will be in a decade or two. Next time, I’ll probably write about how much it is recommended that you invest for retirement followed by a post on how to invest it.

Here’s some more food for thought: 12 Reasons Why You Should Budget.

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