Compound interest is interest calculated on your original balance and on interest already added to it. That means interest can earn more interest when it stays in an account or is reinvested. The same process can increase a debt balance when unpaid interest is added to what you owe.
For savers, the effect builds over time. At a fixed 10% annual rate, $100 grows to $110 after one year, $121 after two, and $133.10 after three, assuming the interest stays in the balance and before fees or taxes.
What $100 looks like as it compounds
The first year’s interest is $10, or 10% of $100. In year two, the 10% applies to $110, so the balance gains $11 and reaches $121. In year three, interest applies to $121, adding $12.10. The balance reaches $133.10.
That is the practical difference between earning interest on the original amount and earning it on an amount that already includes past interest. The example assumes a fixed rate, annual compounding and no deposits, withdrawals, fees or taxes.
How the compound interest formula works
For a fixed annual rate compounded once a year, the formula is A = P × (1 + r)^t. Here, A is the ending balance, P is the starting principal, r is the annual rate written as a decimal, and t is the number of years. A 10% rate is written as 0.10.
When a nominal annual rate is compounded more than once a year, the formula is A = P × (1 + r/m)^(m×t). In this version, m is the number of compounding periods per year. Monthly compounding uses 12 periods; daily compounding uses the schedule specified by the account or investment terms. The rate convention and compounding schedule need to match the terms being modeled.
Compounding frequency changes the result because interest is added to the balance on a schedule. More frequent compounding can produce a higher balance at the same nominal annual rate, all else equal. The effect depends on the rate, the time period and the product’s terms.
A matched example: monthly, annual and simple interest
Consider a hypothetical $5,000 balance at a 5% nominal annual rate for 10 years. With monthly compounding, the ending balance is about $8,235.05. With annual compounding, it is about $8,144.47. With simple interest, which applies interest only to the original principal, it is $7,500. These calculations exclude fees, taxes, deposits, withdrawals and rate changes.
| Calculation method | Ending balance after 10 years |
| Simple interest at 5% annually | $7,500.00 |
| Compound interest at 5% annually | $8,144.47 |
| Compound interest at 5% nominal annually, compounded monthly | $8,235.05 |
In this example, monthly compounding produces about $90.58 more than annual compounding. That difference comes from the schedule, not a higher stated nominal annual rate. Actual account terms determine how interest is calculated and credited.
Simple interest and compound interest use different bases
Hypothetical calculation: a $5,000 starting balance at a fixed 10% annual rate for three years. Compound interest is credited and reinvested annually; simple interest is calculated only on the original $5,000. No deposits, withdrawals, fees or taxes; this is not a bank offer.
| Year | Simple interest earned ($) | Simple-interest total ($) | Compound interest earned ($) | Compounded balance ($) |
| 1 | 500.00 | 5,500.00 | 500.00 | 5,500.00 |
| 2 | 500.00 | 6,000.00 | 550.00 | 6,050.00 |
| 3 | 500.00 | 6,500.00 | 605.00 | 6,655.00 |
Simple interest applies each period’s rate to the original principal. Compound interest applies it to the principal plus interest already added to the balance. With a fixed rate and unchanged principal, simple interest adds the same amount each period; compound interest can add larger amounts as the balance grows.
Why keeping or reinvesting interest matters
Interest has to remain in the account or be added back to the investment for later interest to build on it. If you withdraw the interest, future growth no longer compounds on the withdrawn amount. In an investment, reinvesting distributions or gains can create compounding, but investment returns vary and are not guaranteed.
Regular deposits add another factor: each deposit has a different amount of time to earn returns. A monthly contribution made early in a long-term plan has more periods to compound than one made near the end. The single-deposit formula does not by itself calculate a series of contributions.
What compound interest means for savings, investments and debt
For a savings account, check the rate, how often interest is calculated, when it is credited to the balance, and whether fees or taxes affect what remains. Inflation also matters because it reduces what money can buy over time. A projected account balance is not the same as its future purchasing power.
For an investment, the fixed-rate formula is a model, not a promise. Market returns can change, and fees, taxes and withdrawals affect how much stays invested and can compound.
For a loan, unpaid interest can increase the balance when the loan’s terms add it to principal. Not every loan uses compound interest, so the contract and repayment schedule determine how interest is applied. If you are comparing debts, check whether interest is capitalized and how often the balance is recalculated.
Two useful estimates, not guarantees
The Rule of 72 gives a rough estimate of how long a balance might take to double under a steady annual rate: divide 72 by the rate expressed as a percentage. At 6%, the estimate is about 12 years. It is a shortcut, not an exact forecast, and changing returns or fees alter the outcome.
A steady 7% annual rate compounded for 10 years multiplies a starting balance by about 1.97, not exactly two. Both calculations assume a fixed rate and compounding schedule; they do not predict investment performance.
