If You Had Brought $1 Dollar to the Bank in 0 AD …
… how much would you have now?
Let me make some assumptions to answer the question that are not realistic, but at least conceivable: There were dollars in 0 AD, and they were the same as today and also as at any time in between. There was also no inflation, so we have “nominal = real.”
What is a bit tricky is that you cannot expect a lot of interest for a short-term deposits. Actually, you would have gotten about 0 % in real terms historically. But then you could perhaps buy a ten-year bond from the bank that pays you a regular coupon. Let me assume that it would have been riskless. Riskless long-term bonds have yielded like 2% in real terms historically. You would then roll the bond over into another ten-year bond when it matures.
Long story short: Let’s assume you can get 2% annual interest in real terms on your deposit with the bank.
Now, this type of example is usually meant as a demonstration of how fast compound interest works. And I think it puzzles a lot of people who wonder why noone was so clever to bring one dollar to the bank long ago.
With compound interest you get this:
In 0 AD, you have $1, in 1 AD you have $1.02, in 2 AD you have $1.02 * 1.02 (let’s assume, the bank also works with fractions of a cent), in 3 AD you have $1.02 * 1.02 * 1.02. Or generally, you have $1.02 to the N-th in year N AD with compound interest. That looks innocuous because you start with only one dollar and 2% does not seem like a lot of interest.
However, it takes only 35 years for your dollar to become two dollars, still not a lot. But then the amount doubles once more over the next 35 years to four dollars, then again over the following 35 years to eight dollars, and so on.
That is parallel with the famous story of the man who had invented the game of chess and asked for one rice corn on the first field, two on the next, then four, eight, sixteen, and so forth. Although it looks like nothing, as far as I know, there would not be enough rice in the world for the 64th field.
It is almost as bad here because in the year 2018 AD, you have almost 58 doublings of your initial dollar. If you do the math: $1.02²⁰¹⁸ is an incredible amount of about 226,541 trillion dollars, way more than the whole annual GDP of the world today, which stands at only a meager 75 trillion dollars.
But here is the trick. That is with compound interest! However, nowhere did I assume that you could compound your interest, ie. reinvest it at a rate of 2% annually. I hope you have not already started to make plans with your new-found wealth because under my assumptions the correct answer to the question above is disappointing:
You have one dollar that pays you two cents a year!
Of course, you could have been able to reinvest your interest for some time, so you might have more. But then the bank will simply not accept any more at a rate of 2% from some point on because there would be no investments that could yield such a return for them. Either they would go down to 0% with their offer or or they wish you good luck with finding another bank.
Sorry.
