Hi and welcome to the Matladpi blog! In this post I will concentrate on compound interest, especially the math behind it.

Compound interest has been called one of the wonders of our world. And it is no wonder, at least to those who know the math.

Let us have an example. You invest 1000 dollars into an index fund that, for some reason, guarantees a 10% yearly interest rate, inflation and index fund fees adjusted. Now, you let your money sit there for 40 years. Guess how much you have there after this time is over? Over 45 000 dollars!

Let us now consider an 11% yearly interest rate. After the same time you would have over 65 000 dollars sitting in the index fund! By only increasing your interest rate by one percentage unit, you would get over a 43% increase in your index fund money! Pretty neat how compound interest works, eh?

But this only gets better! Let us assume that you invest 1000 additional dollars yearly (but not in the first year where you started with putting your 1000 dollars in the index fund), before the interest takes effect on that particular year. Now, with 10% and 11% interest rates and after 40 years, you would have over 450 000 and 645 000 dollars in the index fund, respectively!

In other words, by committing yourself by investing additional 1000 dollars a year into the index fund, you would multiply your index fund money by over/almost 10 (compared to the sums of the first two examples)! This is the power of compounding, my friend. Those who know their math may win big time!

What about the math, then? In the first examples you would simply do the following calculations:

1000 × ((1.1)^40) and 1000 × ((1.11)^40), respectively.

Why does the sum grow to such great heights? It is not for vanity called compound interest, as in the compounding you first multiply the 1000 dollars by 1.1/ 1.11 and then multiply the result (!) by 1.1/ 1.11 and then multiply the result by 1.1/ 1.11 etc. and repeat one multiply cycle for 40 times. Thus, you get the final results so large. Also, this large growth process is an example of the power of the powers!

A clear example of powers would also be the number two. What do you think 2^10 is? How about 2^20, or 2^30? Well, they are over 1 000, 1 000 000 and 1 000 000 000, respectively!

The answers to the constant investment commitments can be calculated in the following way:

Use the recursion argument ans in the calculator and write the following lines:

0 (press enter, ans will get to 0)

(ans + 1000)×1.1 or

(ans + 1000)×1.11 (in any one of the both, press enter 40 times in a row).

Thus you will get the results.

!!!

Notice that I am not suggesting or advicing you to invest in anything, these are just ideal examples and the real world scenario could be anything else than this. Actually, you may even lose money by investing, so always think things through before investing. Njäf! said.

I am Jesse Sakari Hyttinen and I will see you in the next post!