Expanding Our Understanding of TVM

We can keep going with this concept and compare $100 today to two years from now, three years, and so on

If we do that through a multi-year exercise, the discounting will be compounded. Compounding is one of the most important concepts in all of finance. It is so important that Albert Einstein himself took notice of the power of the laws of compounding

In our last example, at the end of year one, $100 turned into $95.24 with a 5% discount rate. For year two, you will discount 5% off $95.24 (not $100!), giving you $90.70 at the end of year two. Notice that this is not the same as simply taking 10% off $100 for two years worth of calculating - don’t do that when dealing with TVM.

Compounding is probably more intuitive when thinking in terms of investment returns. Let’s say we take that same $100 but invest it somewhere that gives us 5% return annually. 5% of $100 is $5, but due to the impact of compounding, you will earn far more than $5 per year over time, since each year you are compounding the returns off a higher and higher base.

Take a look at the impact of compounding below, showing the growth of $100 at 5% annually vs. the growth of $100 at $5 annually. Importantly, compounding is exponential, meaning that its impact grows in magnitude as you move farther out in time. After two years, the difference in the two comparisons is $0.25, but after ten years, the divergence increases to $12.89

And to demonstrate what Einstein was talking about in terms of how truly powerful compounding can be, let’s extend that exact same graph out 100 years as a demonstration. Here is what it would look like.

$13,000 vs. $600; now you are truly seeing how powerful compounding can be!