Compound Interest - Economics
Compound interest is the eighth wonder of the world. At its core, compound interest is the interest you earn on interest. When you deposit money into a savings account, the interest earned over a period is added to the principal. In the next period, interest is calculated on the new principal (original principal + accumulated interest). This process continues, and the money grows at an increasing rate due to the effect of compounding.
Compound Interest Formula
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest.
P = the principal investment amount (initial deposit or loan amount).
r = the annual interest rate (in decimal form, so 5% becomes 0.05).
n = the number of times that interest is compounded per year.
t = the number of years the money is invested or borrowed.
The diagram below illustrates the difference between linear and compound growth. Notice how the compound growth accelerates over time, forming an upward curve.
The Rule of 72
The Rule of 72 is a simple way to estimate how long it will take for an investment to double. If money grows at a percentage of R in each period, with all gains reinvested, it will double in approximately 72/R periods. For example, if you have an investment earning 8% annually, it would take about 9 years (72/8) for your money to double. You can verify this since (1 + 0.08)^9 ≈ 2.
Compound Interest in Everyday Life
Health: Regular exercise, such as running, hiking, walking, or playing tennis for six to eight hours a week, can have compounding long-term health benefits. Each workout builds upon the previous one, leading to increased fitness, longevity, and overall well-being.
Bad Habits: Negative behaviours also compound. Smoking a pack of cigarettes daily, for instance, doesn't just affect your health linearly—the damage compounds over time, significantly increasing health risks.
Reputation: As Naval Ravikant puts it, "If you have a sterling reputation and you keep building it for decades upon decades, people will notice." Each positive interaction or successful project builds upon your previous accomplishments, compounding your professional reputation and opportunities.