Compound Interest
Use the Compound Interest Calculator → Try the Compound Interest Quiz →Compound interest is interest calculated on both the original principal and all accumulated interest from prior periods. It causes wealth to grow exponentially over time - and debt to escalate at the same pace if left unpaid.
- Compound interest earns interest on previously earned interest, not just on the original principal - creating exponential rather than linear growth over time.
- A 12% annual rate compounding monthly has an effective annual rate (EAR) of 12.68% - the true annual cost, which is always higher than the stated nominal rate when compounding is more frequent than annually.
- Monthly compounding of $10,000 at 6% over 20 years produces $33,102 versus $32,071 with annual compounding - a $1,031 difference from compounding frequency alone.
- The Rule of 72: divide 72 by the annual interest rate to estimate the number of years required to double your money (72 ÷ 6% = 12 years to double).
- Compounding works against borrowers on debt: credit card debt at 20% APR compounding monthly grows a $1,000 balance to $2,653 after 5 years with no payments.
$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
What is Compound Interest?
Compound interest is interest calculated on the accumulated balance, not just the original principal. Each period, the interest earned is added to the principal, and the next period's interest is then earned on this larger combined balance. This creates a compounding feedback loop: the more you have, the more you earn, the more you have.
The standard formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years. Monthly compounding (n = 12) produces a slightly higher return than annual compounding (n = 1) for the same stated annual rate.
Compounding frequency matters significantly over long time horizons. $100,000 invested at 8% per year for 30 years grows to $1,006,266 with annual compounding, but to $1,020,808 with daily compounding - a difference of $14,542 simply from the compounding schedule. At higher rates and longer periods, this gap widens substantially.
Compound Interest explained to a beginner
Imagine a snowball rolling downhill. It starts small, but as it rolls, it picks up more snow - and the bigger it gets, the more snow it picks up each rotation. Compound interest works the same way: your money earns interest, that interest is added to your balance, and next period your larger balance earns even more interest.
The practical implication is time is your most powerful lever. $10,000 invested at 7% for 10 years grows to about $19,672. Leave it for 30 years and it becomes $76,123 - nearly four times more, from twice as many years. Starting 10 years earlier often matters more than saving more money later.
When to use Compound Interest
Use compound interest calculations for any long-term savings, investment, or debt scenario. For investments, use it to project what a lump sum grows to, or reverse-engineer the rate required to reach a target. For debt (mortgages, credit cards, student loans), compound interest explains why carrying balances is so costly - interest accrues on interest.
Worked examples for Compound Interest
This table quickly gives you the overview you need to understand Compound Interest and its most important comparisons.
| Principal | Rate | Compounding | Years | Final Balance | Total Interest |
|---|---|---|---|---|---|
| $10,000 | 6% | Annual | 20 | $32,071 | $22,071 |
| $10,000 | 6% | Monthly | 20 | $33,102 | $23,102 |
| $50,000 | 8% | Monthly | 30 | $544,572 | $494,572 |
| $1,000 | 20% (credit card) | Monthly | 5 | $2,653 | $1,653 |
Common pitfalls
Do not confuse nominal and effective interest rates. A 12% annual rate compounding monthly has an effective annual rate (EAR) of 12.68% - this is the true annual cost of borrowing. Lenders are typically required to disclose APR (Annual Percentage Rate), which may or may not reflect compounding depending on jurisdiction. Always check whether a quoted rate is nominal or effective.
$10,000 invested at 8% for 30 years grows to approximately $100,627 with annual compounding - the compound interest alone ($90,627) is more than 9 times the original principal, illustrating why Einstein reportedly called compounding "the eighth wonder of the world." (Standard compound growth calculation)
Frequently asked questions about Compound Interest
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal: Interest = P × r × t. Compound interest is calculated on the principal plus all previously accumulated interest. For short periods and low rates, the difference is minimal. Over decades, the gap becomes enormous - simple interest grows linearly, compound interest grows exponentially.
How does the Rule of 72 relate to compound interest?
The Rule of 72 is a mental shortcut for compound interest: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in approximately 12 years (72 ÷ 6). At 9%, it doubles in roughly 8 years. This works because of the mathematical properties of the compound interest exponential.
Does compound interest apply to stocks?
Not directly - stocks do not pay a fixed interest rate. But the concept of compounding applies to investment returns through reinvested dividends and retained earnings that generate future earnings. The term "compounding" in equity investing refers to the same exponential growth principle, applied to variable returns.
Quiz: how well do you know compound interest?
1. What makes compound interest different from simple interest in how it calculates each period's interest?
2. According to the FAQ, how does compound interest growth differ from simple interest growth over long periods?
3. From the worked examples table, what is the final balance for $10,000 invested at 6% with monthly compounding over 20 years?
4. According to the pitfalls section, what is the effective annual rate (EAR) of a 12% annual rate that compounds monthly?
5. The FAQ explains the Rule of 72 as a compound interest shortcut. Using it, approximately how many years does money take to double at a 9% annual rate?