How to Calculate Compound Interest
Compound interest describes growth when interest is added to a balance and future interest is calculated on the larger amount. The effect can be small over short periods but substantial over long horizons. This guide explains the standard compound interest formula, a worked example, compounding frequency, regular contributions, and common projection mistakes.
Last reviewed: 2026-08-29
Compound interest formula
For an initial amount that compounds at a fixed rate without additional deposits or withdrawals, use the standard future value formula:
- A = P × (1 + r ÷ n)^(n × t)
- Compound Interest = A − P
A is the ending balance, P is the starting principal, r is the annual interest rate written as a decimal, n is the number of compounding periods per year, and t is the number of years.
You can enter these values directly in the Compound Interest Calculator to estimate future value and total growth.
Compound interest example
Suppose you start with $10,000, earn a fixed 6% annual rate, compound monthly, and leave the balance untouched for five years.
- A = 10,000 × (1 + 0.06 ÷ 12)^(12 × 5)
- A ≈ $13,488.50
- Compound Interest ≈ $3,488.50
The ending balance is about $13,488.50. The difference between that balance and the original $10,000 is the interest generated under these assumptions.
Why compounding creates growth on growth
With simple interest, interest is calculated from the original principal each period. With compound interest, credited interest becomes part of the balance. Later periods can therefore generate returns on both the original principal and previously credited interest.
This is why time is an important variable. Compounding has more opportunities to build on earlier growth when money remains invested or deposited for longer.
How compounding frequency changes the result
The variable n represents how often interest is compounded. Annual compounding uses n = 1, quarterly uses n = 4, monthly uses n = 12, and daily compounding commonly uses n = 365 when that convention applies.
At the same nominal annual rate, more frequent compounding generally increases the ending balance slightly because credited interest begins participating in subsequent periods sooner. Always match the frequency in your calculation to the terms of the account, loan, or scenario you are modeling.
Compound interest with regular contributions
Many real savings and investment plans include recurring deposits. In that case, the starting principal is only one source of future value. Each new contribution has its own compounding period: an early contribution normally has more time to grow than one made near the end of the projection.
For planning, specify whether contributions occur at the beginning or end of each period. That timing changes the result. Also keep the contribution interval consistent with the model—for example, monthly deposits with monthly periods.
Annual rate vs periodic rate
A common error is inserting a percentage directly into the formula. A 6% annual rate must be written as 0.06. When compounding monthly, the standard formula divides that annual decimal rate by 12 to obtain the periodic rate.
If you need help converting a percentage to its decimal form or calculating percentage changes, use the Percentage Calculator.
Nominal rate and effective annual growth
A quoted nominal annual rate and the effective annual growth produced by compounding are not always identical. For example, a nominal rate compounded monthly can result in an effective annual rate that is slightly higher than the nominal rate. When comparing financial products, make sure the rates you compare use compatible definitions.
Common compound interest mistakes
- Using 6 instead of 0.06 for 6%. Percentages must be converted to decimals in the formula.
- Mixing time units. The compounding frequency and time horizon must use compatible periods.
- Ignoring contribution timing. Beginning-of-period and end-of-period deposits do not produce exactly the same future value.
- Treating a projection as a guarantee. Variable investment returns, fees, taxes, withdrawals, and rate changes can materially alter actual outcomes.
- Comparing incompatible rates. Nominal rates, effective rates, APR, and APY can describe costs or growth differently.
How to use compound interest projections
Compound interest calculations are most useful for scenario planning. Try several rates, contribution levels, and time horizons rather than relying on one forecast. This shows how sensitive the outcome is to assumptions and makes the calculation more useful for savings goals, long-term planning, or evaluating fixed-rate scenarios.
Explore additional tools in Finance Calculators when you need to compare income or other financial calculations alongside a growth projection.