As a follow up to the two previous posts on government accounting it just so happened that I was reading today that Albert Einstein’s brain was “different” from most of ours. Without going into the specifics (of which I have only a poor grasp), let me just acknowledge that he was a genius – whatever the reasons for that might have been.
Einstein claimed that his greatest discovery was “The Rule of 72”. He happened upon it when he was employed in the patent office as a clerk and had some down time in his duties. The rule is very simple.
If you want to know how long it takes money to double at a specific compound rate of interest, divide the interest rate into 72 for an approximation. In other words, one dollar will double at a rate of one percent interest in approximately 72 years; at two percent in approximately 36 years, at three percent in approximately 24 years, etc.
This rule becomes less accurate the higher the rate of interest – as we can see by inspection. An interest rate of seventy-two percent is not going to double in the expected one year but show an increase of seventy-two percent. The smaller the rate of interest, the more accurate the calculation.
What the rule demonstrates is the power of compounding. That can work either to our advantage or to our detriment.
The handwritten chart below demonstrates this principle at five different interest rates. There is a reason that the chart is handwritten (pardon my calligraphy). Yes, I can use Lotus and Excel spreadsheets. Yes, they look neater. But plugging in formulae and letting a computer do the thinking for us is one of my pet peeves.
You see I believe that, notwithstanding the wonderful achievements we have attained through technology, once in a while it is imperative that we use our own brains to solve problems. Otherwise, we unintentionally wind up dumbing ourselves down – and there is a lot of that going around.
This example assumes that Grandma made a gift to her grandchild in the amount of $100 at the age of sweet 16. The child had the choice of placing this gift in an investment that would yield a consistent return at one of five specified interest rates, ranging between two to twenty-four percent. (You will say, there is probably no investment available that would yield a consistent twenty-four percent and you would be correct. In today’s market environment it’s hard to find an investment that yields a consistent two percent).
This example also assumes that there would have been no tax collected on the increase of the investment during the years from 16 to age 70 when the grandchild cashes in her gift. (Now there’s hallucinatory thinking elevated to its epitome).
So here’s the chart:
As you can see, after fifty-four years of working on behalf of the grandchild, the investment which yielded two percent has now grown to a mere $286. (I computed the difference from age 52 to age 70 manually since this investment required a 36 year period to double). That’s pretty anemic. Of course, the investment at four percent did better – but not twice as well as many would expect. It did almost three times better than its lower tier brother.
And then we get into the shocking return on the eight percent investment. Again, twice the interest rate had the effect of producing eight times the result. And the twelve percent interest rate dwarfed that, providing the beneficiary of Grandma’s original $100 gift by rewarding her with $51,200 in her account. We’ll save discussing the twenty-four percent interest rate for just a bit.
It really is amazing how the difference in the interest rate on an investment coupled with long time periods results in different returns. Unfortunately, most of us are not cognizant of this because we are never taught these principles in our schooling – and many of our parents are as unaware of them as our teachers.
Now there is good news and bad news in all of this. You’re probably correct in believing that receiving a guaranteed return of twenty-four percent a year is un-attainable. And you’re right – unless you happen to be a bank that issues credit cards to less than top notch borrowers. A twenty-four percent interest rate on unpaid balances is not unusual for people who fall into that category.
So instead of an investment, let’s think of this $100 as a loan. The bank which issues it is very generous. They are making it for a 54 year period – and the terms (other than the rate of interest) are very beneficent. Nothing will be due until the loan recipient reaches age 70 – at which point the principal and interest will become payable in full.
As you can see from the chart, this $100 loan and accrued interest has grown to the staggering amount of $26,214,400. Egad! And that is the negative effect of compound interest.
After reviewing and, I hope, thinking about this for a bit, you will perhaps understand why the American consumer has gotten herself into very muddy waters with credit card debt. But that is merely the tip off the iceberg.
We have a government that has similarly encumbered itself (and all of us) in the same problem.
It is estimated that the interest that will be due on our National Debt for calendar year 2012 will be approximately $360,000,000,000. For those of you who, like me get lost with all those zeroes, that’s $360 Billion. Take into account, that amounts to an interest rate of only 2.25% of our current outstanding balance – even with the Federal Reserve’s current policy of artificially suppressing interest rates. The reason the effective interest rate is this high is because a significant amount of this debt was issued at higher rates than the one quarter of one percent rate that is currently in effect.
So if you want to think about an apocalyptic event, consider what a return to normal interest rates, (in the area of 3 – 5 %) would mean in terms of the amount of money that would be required to pay the interest on our $16 Trillion National Debt balance.
And that’s why, when you hear people say that we have encumbered ourselves and our children and our grandchildren with an almost unresolvable problem – short of default – they have a serious point that they are making.
And on that happy note, I’m going to spend a bit of time reading and then head off to slumber land – thinking about the National Debt and Albert Einstein.
Darn, that guy was smart.