1. compound growth

We all know the power of compound interest and time. For example, a $10,000 investment grow at 10% annual return over 40 years might sound like it can grow to $50,000. In reality, it would actually grow to $$452,592.56

Let's assume our principle is X, and our annual return rate is r

After 1 year, we would have X * (1+r)

After 2 years, we would have X * (1+r) * (1+r)

After 3 years, we would have X * (1+r) * (1+r) * (1+r)

We can already see the pattern here. Therefore,

After n years, we would have X * (1+r)^n

Going back to our example, $10,000 investment grow at 10% annually over 40 years would be worth

$10,000 * (1+10%)^40 = $452,592.56

It's interesting to note that the original investment is actually the least important variable in the equation since it's a linear component. For example, half the investment will result in exactly half the future value.

$5,000 * (1+10%)^40 = $226,296.28

The interest rate and time, on the other hand, can causes much bigger changes. For example, half the interest rate would lower the future value to only about 7 times.

$10,000 * (1+5%)^40 = $70,399.89

Similarly, half the investment time would lower the future value even more

$10,000 * (1+10%)^20 = $67,275.00