The Core Idea
Simple interest pays you only on the money you put in. Compound interest pays you on the money you put in plus every dollar of interest it has already earned. Each period, the base grows, so the growth itself grows. It starts slow and ends dramatic.
Take $1,000 at 8% annual growth. After one year: $1,080. After year two, you earn 8% on $1,080, not $1,000, so you land at $1,166.40. By year 20, that single $1,000 is about $4,661. The interest earned in year 20 alone ($345) is more than a third of the original deposit. That acceleration is compounding doing the heavy lifting. Notice the curve: growth in the first five years is modest, but the last five years do most of the work. This back-loaded shape is why patience matters more than timing.
The Compound Interest Formula
The formula is A = P(1 + r/n)^(nt). P is the starting principal. r is the annual rate as a decimal (8% = 0.08). n is how many times interest compounds per year: 12 for monthly, 4 for quarterly, 1 for annual. t is the number of years. A is what you end up with.
Compounding frequency matters, but less than people think. At 8% for 10 years, $1,000 compounded annually becomes $2,159; compounded monthly it becomes $2,220. A real difference, but tiny next to what the rate and the time do. Time is the variable that dominates everything.
The Rule of 72
For a quick mental estimate, divide 72 by your annual return to get the approximate number of years until your money doubles. At 8%: 72 / 8 = 9 years. At 6%: 12 years. At 12%: 6 years.
The Rule of 72 is an approximation, accurate within a year or so for returns between 4% and 12%. It is useful because it makes the abstract concrete: at 10%, your money doubles roughly three times in 25 years, which means $10,000 becomes about $80,000 with no additional contributions.
Why Starting Early Beats Investing More
This is the example that converts skeptics. Two people each invest $5,000 per year at 8% average growth. Person A starts at 25 and stops at 35, ten years, $50,000 total in. Person B starts at 35 and keeps going to 65, thirty years, $150,000 total in.
At 65, Person A has about $790,000. Person B has about $612,000. Person A invested one-third the money and ended up with more, because their dollars had ten extra years of compounding. Every year you wait costs you twice: the contribution you did not make, and all the compounding that contribution would have produced.
Frequently Asked Questions
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate as a decimal, n is how many times interest compounds per year, and t is the number of years. A is the final amount.
What is the Rule of 72?
Divide 72 by your annual return to estimate how many years it takes your money to double. At 8% annual growth, 72 / 8 = 9 years to double. It is an approximation that works best for rates between 4% and 12%.
How is compound interest different from simple interest?
Simple interest pays only on the original principal. Compound interest pays on the principal plus all previously accumulated interest, so the balance grows faster every period. Over long timeframes the gap is enormous.
Does compounding frequency matter?
Somewhat. Monthly compounding beats annual compounding, but the difference is small compared to the effects of a higher rate or more time. Continuous compounding is the mathematical limit, and it only adds a small boost over monthly.