Interest on principal and prior interest
Simple interest applies a rate only to the starting principal. Compound interest updates the balance after interest is credited, so later calculations can include earlier interest. The difference may be small over a short period and more noticeable over many periods.
Compounding frequency describes how often interest is added under the model. A quoted annual rate and an annual percentage yield are not interchangeable: APY reflects compounding under its stated assumptions, while a nominal annual rate may not. Use the measure and frequency specified by the account or projection.
The compound interest formula
For a single initial deposit with a constant nominal annual rate, no withdrawals, and regular compounding, the standard formula calculates the future balance. Interest earned is the future balance minus the original principal.
Regular contributions require an additional future-value calculation, and timing matters: deposits at the beginning of each period have one more period to compound than deposits at the end.
Worked example: a five-year savings projection
Assume $10,000 remains in an account for five years at an illustrative 4% nominal annual rate, compounded monthly. This constant rate is chosen only to show the calculation and is not a current account offer.
Contributions, withdrawals, and time
Regular contributions can become a major part of an ending balance. Keep contributed principal separate from growth so a projection shows what was deposited and what the assumed return generated. Apply withdrawals on their actual modeled dates because removing funds also removes their potential future compounding.
Time increases the number of compounding periods, but it does not remove uncertainty. For variable-rate accounts or investments, a smooth constant rate is a simplifying assumption. Comparing several rates can show sensitivity without implying that any one path will occur.
Read a projection in today’s context
A nominal ending balance is not the same as purchasing power. Inflation can reduce what that amount buys. Fees and taxes may reduce the balance or return, while deposit or withdrawal timing can move the result in either direction.
Use projections to understand relationships and test inputs. For a real account, review its rate definition, compounding and crediting rules, fees, restrictions, tax treatment, and protections rather than relying on a generic formula alone.
Assumptions and limitations
Assumptions used in the explanations
- The example rate stays constant and interest compounds monthly.
- There are no deposits, withdrawals, fees, taxes, or interrupted compounding.
- The rate is a nominal annual rate divided evenly across 12 monthly periods.
What this guide cannot tell you
- Actual account rates and investment returns can change and may be negative in some products.
- The basic lump-sum formula does not model irregular cash flows, tiers, fees, taxes, or account-specific crediting rules.
- Nominal projections do not show inflation-adjusted purchasing power or guarantee an outcome.
This guide provides general educational information, not financial, tax, legal, or lending advice.
Frequently asked questions
How is compound interest different from simple interest?
Simple interest is calculated only on the original principal. Compound interest can be calculated on principal plus interest credited in earlier periods.
Does more frequent compounding always create a higher balance?
With the same nominal annual rate and otherwise identical assumptions, more frequent compounding produces a slightly higher modeled balance. Offers may quote rates differently, so compare effective yields rather than frequency alone.
Can the formula include monthly contributions?
The displayed formula covers one lump sum. Contributions need a future-value-of-a-series formula, with an adjustment based on whether each contribution occurs at the beginning or end of a period.
Why might an actual balance differ from the projection?
Rates can change, deposits and withdrawals may occur on different dates, and fees, taxes, rounding, or account rules may alter credited interest.