Free calculator

Compound Interest Calculator

Estimate savings growth from an initial amount and recurring deposits, with independent compounding frequency, deposit timing and a yearly breakdown.

Calculations stay in your browser. These are mathematical projections, not investment advice. Actual returns may differ; market volatility, taxes, fees, inflation and withdrawals are excluded.

How to use this tool

Project an ending balance and separate the money you deposit from estimated compound growth using a constant nominal annual rate.

Transparent method

Formula and method

Without deposits: A = P × (1 + r/n)^(n×t), where P is principal, r is the annual decimal rate, n is compounding periods per year and t is years. Between deposits, the growth rate is (1 + r/n)^(n/f) − 1, where f is deposits per year.

Example

Start with $10,000 at 5% nominal annual interest, compounded monthly, and add $250 at each month end for ten years. The estimated balance is $55,290.66: $10,000 principal + $30,000 deposits + $15,290.66 growth.

Assumptions and limits

The nominal annual rate and deposit amount remain constant. Negative rates and withdrawals are not supported.
Use whole years from 1 to 100 and rates from 0% to 100%. Daily compounding means 365 equal periods per year, without calendar or leap-day adjustments.
Growth between deposits uses equivalent fractional compounding periods. Actual bank accrual and crediting conventions can differ.
Beginning and end timing use the same number of deposits: years × deposit frequency. A zero recurring amount means zero deposits.
USD, GBP and CAD change formatting only. No exchange-rate conversion occurs.
Full numeric precision is retained internally; displayed money is rounded to cents. Displayed parts can differ from their total by a cent.
This mathematical projection excludes market volatility, taxes, fees, inflation, variable returns and withdrawals. It is not investment advice or a guaranteed return.

What compound interest means

Compound interest is growth earned on both your original principal and interest already accumulated. Contributions add new money to the balance; interest is the additional amount generated by the assumed rate. The calculator separates those amounts so deposits are not mistaken for investment returns.

Compound interest formula and nominal rate

The principal-only formula is A = P × (1 + r/n)^(n×t). Enter 5 for a 5% rate; the calculation converts that percentage to 0.05 before dividing by the chosen compounding frequency. The entered rate is nominal, not an already-compounded annual yield.

For deposits, each contribution period first adds a beginning deposit if selected, applies its equivalent growth rate, then adds an end deposit if selected. The yearly table records those same calculations, rather than using a separate estimate.

Compounding frequency versus contribution frequency

Compounding frequency sets how the nominal annual rate compounds: annually, semiannually, quarterly, monthly or daily using 365 periods. Contribution frequency determines how often new money is added: monthly, quarterly or annually. These settings are independent; monthly compounding can be combined with annual deposits.

Mixed frequencies use (1 + r/n)^(n/f) − 1 as the growth rate between deposits. This equivalent fractional-period convention credits growth proportionately in time; it does not reproduce a particular bank's daily balance or interest-crediting rules.

Beginning versus end contributions

A beginning deposit receives growth during its contribution period. An end deposit starts growing during the following period. Over ten whole years, monthly deposits occur exactly 120 times and annual deposits exactly ten times under either timing setting.

Beginning deposits start at time zero and stop one period before the end. End deposits start after the first period and include the final boundary. Changing timing does not add an extra deposit.

Understanding the yearly growth table

Each row shows the starting balance, new contributions, interest or growth, and ending balance for a complete year. The previous year's ending balance becomes the next year's starting balance. Total recurring contributions excludes the initial principal.

Starting principal + total recurring contributions + total growth equals the ending balance before display rounding. The calculator supports whole years only, so no partial year is presented as a complete year.

Monthly versus annual compounding and effective annual rate

At the same positive nominal rate, more frequent compounding produces more principal-only growth. Effective annual rate measures this effect: EAR = (1 + r/n)^n − 1. At 5% nominal with monthly compounding, the effective annual rate is approximately 5.1162%.

The effective annual rate shown here excludes fees, taxes and other product terms. Compare rates with the same definition; entering an effective annual rate as a nominal rate can overstate growth.

Verified compound growth examples

Principal only: $10,000 at 5% compounded annually for ten years becomes $16,288.95, including $6,288.95 growth.

Monthly deposits: $10,000 at 5% compounded monthly with $250 deposited at each month end for ten years becomes $55,290.66. Deposits total $30,000 and growth is $15,290.66.

Beginning versus end: moving those same 120 deposits to each month's beginning gives $55,452.42, compared with $55,290.66 for month-end deposits.

Different compounding: $10,000 at 5% for ten years with no deposits becomes $16,470.09 with monthly compounding, compared with $16,288.95 with annual compounding.

Zero interest: starting from $0 and adding $250 monthly for ten years produces exactly $30,000 in deposits and $0 growth.

Simple interest and the Rule of 72

For an unchanged principal, simple interest applies the rate only to that original amount. Compound interest also earns growth on accumulated interest. With no deposits, $10,000 at 5% simple interest for ten years would become $15,000; annual compounding gives $16,288.95.

The Rule of 72 estimates doubling time as 72 divided by the annual rate percentage. At 6%, it suggests about 12 years. It is an approximation, does not account for recurring deposits, and is never used for this calculator's results. It is undefined at 0%.

Common mistakes and projection limits

Enter the amount per deposit, not the annual total when selecting monthly deposits. Match the nominal rate and compounding convention, distinguish new deposits from growth, and check contribution timing before comparing results.

A constant positive rate is a mathematical assumption. Investments can lose value and savings rates can change. This tool does not model volatility, taxes, fees, inflation, withdrawals, risk or product-specific terms; it cannot determine a suitable investment or guarantee a future balance.

Sources

SEC Investor.gov — Compound Interest Calculator

Frequently asked questions

How is compound interest calculated?

Without deposits, A = P × (1 + r/n)^(n×t). P is principal, r is the annual decimal rate, n is compounding periods per year and t is years. Recurring deposits are added at the selected beginning or end of each contribution period.

What is the difference between compounding and contribution frequency?

Compounding frequency controls how the nominal rate grows the balance. Contribution frequency controls when you add money. They can differ, using equivalent fractional-period growth between deposits.

Does contributing at the beginning or end matter?

At a positive rate, beginning deposits earn an extra contribution period of growth. Both settings make the same number of deposits; ten years of monthly contributions means 120 deposits.

Does monthly compounding earn more than annual compounding?

For the same positive nominal rate and principal without withdrawals, monthly compounding produces more growth than annual compounding. At 0%, frequency makes no difference.

Can I start with no initial savings?

Yes. Start at zero and add recurring deposits. If both principal and deposits are zero, the result is zero.

Does total contributions include the initial amount?

No. Total recurring contributions counts only new deposits. Starting principal is shown separately, and both are added to growth to obtain the ending balance.

Can I use fractional years or negative rates?

This calculator accepts whole years from 1 to 100 and non-negative nominal rates up to 100%. Partial years, negative rates and withdrawals are outside its scope.

What is the Rule of 72?

It approximates doubling time by dividing 72 by the annual rate percentage. It does not account for recurring deposits and is not used to calculate these results.

What is simple interest versus compound interest?

Simple interest on an unchanged principal applies only to that principal. Compound interest also earns growth on accumulated interest.

Does this calculator include taxes, fees or guaranteed returns?

No. It is a mathematical projection at a constant rate, excluding taxes, fees, inflation and market volatility. Actual savings and investment returns can differ and are not guaranteed.