How compound interest works and how your savings grow: simple vs compound interest, and the Rule of 72
Compound interest means interest added on top of interest — "interest on interest." It makes savings grow faster over time, but the same rule works against you on debt. This explainer covers the difference between simple and compound interest, the formula, the Rule of 72 and concrete examples, on the basis of sources. This is not financial advice.
Compound interest is one of the most important ideas in personal finance. Put simply, it is interest added on top of interest. As a result, savings grow faster as the years pass. Below the concept is set out as sourced facts and concrete examples only; this is not financial advice.
Simple vs compound interest
With simple interest, interest is charged only on the original amount (the principal). With compound interest, interest is charged on the principal and on previously accumulated interest — the US Securities and Exchange Commission (SEC) defines it as "interest you earn on interest." For example, at a 5 percent annual rate, $100 becomes $105 after one year; in the second year, interest is charged on $105, not $100.
The formula
The standard formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate (as a decimal), n is the number of compounding periods per year, t is the number of years, and A is the final amount. For example, $1,000 at 5 percent compounded once a year reaches $1,628.89 after 10 years.
Compounding frequency matters
The more often interest is compounded (daily > monthly > annually), the larger the final result. For example, $10,000 at 5 percent over one year: compounded annually — $10,500.00; compounded monthly — $10,511.62; compounded daily — $10,512.67. The theoretical limit is "continuous" compounding (A = Pe^(rt)), which gives $10,512.71.
The Rule of 72
The Rule of 72 is a quick way to estimate how long it takes money to double: years to double ≈ 72 ÷ the annual interest rate (in percent). For example, at 6 percent, 72 ÷ 6 = 12 years. The precise calculation gives 11.9 years — so the Rule of 72 is a very close approximation, not an exact formula.
Time is the biggest driver
In compound interest the biggest force is time. The earlier you start saving, the more time there is for interest to pile on interest. Example: $1,000 at 5 percent over 10 years reaches $1,628.89 compounded annually, and $1,647.01 compounded monthly. Even with the same amount and rate, a longer horizon and more frequent compounding raise the result noticeably.
APR and APY
Advertisements and contracts show two figures. APR (the nominal annual rate) usually does not account for compounding; APY (the annual percentage yield) does account for compounding frequency. So when interest is compounded more than once a year, APY is always higher than APR. For example, a 5 percent nominal rate compounded monthly gives an APY of about 5.12 percent. When comparing savings, it is more accurate to look at APY.
Interest also works against you on debt
Compound interest works not only in favor of savings but also against you on debt. According to the US Consumer Financial Protection Bureau (CFPB), interest on credit cards is often added to the balance every day — that is, interest compounds daily and the debt grows. This is why paying off debt as quickly as possible protects you from the downside of compounding.
Conclusion
Compound interest is a simple but powerful rule: interest is added on top of interest, and growth speeds up over time. For savings this is an advantage; for debt it is a danger. The exact terms, rate and compounding frequency vary by bank and product, so check the APY and the terms before deciding.
