Week 3 Day 1: Interest on Interest

You deposit $1,000. It earns 7%, so you now have $1,070. Next year, you earn 7% on $1,070 -- not just the original $1,000. That extra $4.90 does not sound like much. But repeat this for 30 years and the snowball becomes an avalanche. The money does the heavy lifting.

Here is the key insight most people miss: compounding is not linear. It is exponential. The first 10 years feel slow. The next 10 feel faster. The last 10 are explosive. On a $10,000 investment at 7%: after 10 years you have $19,672. After 20 years: $38,697. After 30 years: $76,123. Notice that the portfolio gained roughly $10,000 in the first decade, $19,000 in the second decade, and $37,000 in the third. Same rate. Same person. But the later decades produce nearly 4x the growth of the first decade because there is so much more money compounding. This is why starting early matters more than starting big.

Albert Einstein is often quoted as calling compound interest the 'eighth wonder of the world.' While the attribution is likely apocryphal, the mathematical reality is not. The compound interest formula -- A = P(1 + r)^n -- is an exponential function where time (n) is the exponent. This means time is the most powerful variable in the equation, not the principal (P) or the rate (r). Doubling your time horizon has a far greater impact than doubling your contribution. A 25-year-old investing $200/month for 40 years at 7% accumulates roughly $525,000. A 45-year-old would need to invest $1,050/month for 20 years to reach the same amount. The 25-year-old contributed $96,000 total. The 45-year-old contributed $252,000. Time gave the younger investor a $156,000 discount.