Things every young person needs to know about money - Chapter 4 – The Time Value of Money
“Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.” Albert Einstein
“If you understand compound interest, you basically understand the universe.” Robert Breault
A dollar today is worth more than a dollar tomorrow.
Those simple words are a core principle of finance, and without it your possessions would be limited to what you could pay cash for at any given moment. What is your home worth? Did you have that much cash in the bank, or did you borrow the money? What about your car?
In pure economic terms, the dollar of tomorrow is less than the dollar today because of inflation. Inflation is the gradual (usually!) increase in the price of things. If I don’t invest my dollar, it’s value will erode over time. If I put my dollar in a safe for two years, I lose twice! I lose the money I could have earned off that investment and it will have less buying power because inflation will have eroded its value.
Here is another example. Let’s say that you sell something to a friend for $2000. Your friend asks if you will take $1000 now and another $1000 in a year. Should you? Friendship aside, no! The $1000 you receive in year will still have the same face value, but you will have lost purchasing power because of an entire year of inflation. Furthermore, you have lost the opportunity to invest that money!
There is a very simple formula to determine the future value of a an investment. While this may vary slightly based on the variables used, the formula usually takes into account the following data points:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Here is the formula:
FV = PV x [ 1 + (i / n) ] (n x t)
Let’s look at an example where you have $5,000 and can expect to earn 5% interest on that sum each year for the next two years. Assuming the interest is only compounded annually, the future value of your $5,000 today can be calculated as follows:
FV = $5,000 x (1 + (5% / 1) ^ (1 x 2) = $5,512.50
You can make a very simple formula change to compute the present value. Simply swap the PV and FV variables and divide instead of multiplying. Here is the formula:
PV = FV/ [ 1 + (i / n) ] (n x t)
Here is an example of why we might want to compute present value. If I needed $1100 in one year, how much would I need to invest at 5% to achieve that? We can simply plug those values into the formula:
PV = $1,100 / (1 + (5% / 1) ^ (1 x 1) = $1,047
A quick internet search will identify online calculators to quickly solve for present value and future value. You can also program Excel to do the calculation.
Every young person needs to become familiar with these calculations. If you don’t want to learn the math, as a minimum understand the Time Value of Money concept. It will have profound and practical implications for day to day financial decisions.
Next, I’ll discuss the beauty of compound returns.
Why is the Afghanistan withdrawal such a disaster? More specifically, why were such obvious risks not identified and addressed? I believe it is because there was a stunning lack of diversity on the planning team. Diversity isn't just what you look like, it is how you think, your education and your life experiences. If you purge all dissenting ideologies from your leadership team and surround yourself with people who think like you, you create huge blind spots. Your team will quickly sink into groupthink where everyone amplifies each others shared view of reality. I have seen this occur time and time again as terrible decisions are made by educated people who should have known better.