Compound Interest Calculator

A compound interest calculator estimates how an initial balance and regular contributions may grow when returns are reinvested. Advanced planning also needs to account for fees, taxes, inflation, withdrawals and the uncertainty of future returns.

Compound interest means earning a return on both the original principal and previously accumulated interest. Investor.gov and the Consumer Financial Protection Bureau describe the same basic mechanism: interest is added to the balance, so future interest is calculated on a larger amount. The effect becomes more visible as time, the rate and the frequency of compounding increase.

What the calculator includes

• future value of an initial lump sum;
• weekly, biweekly, monthly, quarterly, semi-annual or annual contributions;
• payments at the beginning or end of each period;
• annual growth in the contribution amount;
• one-time deposits and withdrawals;
• nominal and effective annual interest rates;
• continuous, daily, weekly, monthly, quarterly, semi-annual and annual compounding;
• initial, percentage-based and fixed annual fees;
• simplified annual or end-of-term tax estimates;
• inflation-adjusted purchasing power;
• required contribution, rate or time for a target;
• comparison of several scenarios;
• year-by-year tables, charts and CSV export.

Basic compound interest formula

For one initial deposit with no additional cash flows, the standard formula is:

A = P × (1 + r ÷ n)^{n × t}

Where:

• A is the future value;
• P is the initial principal;
• r is the nominal annual rate as a decimal;
• n is the number of compounding periods per year;
• t is the number of years.

The formula assumes a constant rate and no deposits or withdrawals. The calculator uses a detailed simulation when the plan contains changing contributions, costs or dated cash flows.

Continuous compounding

With continuous compounding, the formula becomes:

A = P × e^{r × t}

Continuous compounding represents a mathematical limit rather than a typical retail savings schedule. It can help compare rate conventions, but the product document should determine the rate and crediting method used in a real calculation.

Nominal rate and effective annual rate

A nominal annual rate does not include the full effect of compounding within the year. The effective annual rate, often described as APY in deposit-account disclosures, reflects both the stated rate and the compounding frequency. CFPB regulations describe annual percentage yield as the amount of interest paid based on the interest rate and the frequency of compounding.

The calculator converts a nominal rate with:

Effective annual rate = (1 + nominal rate ÷ periods per year)^{periods per year} − 1.

Why compounding frequency matters

More frequent compounding slightly increases the effective return when the nominal rate stays the same. Monthly compounding normally produces a higher annual result than annual compounding, while daily compounding produces a slightly higher result than monthly compounding.

The difference is often smaller than the effects of time, contributions, fees and risk. Use the method stated by the account or product.

Regular contributions

For equal deposits made at the end of every period, the future value of the contribution stream is:

FV = PMT × ((1 + i)^m − 1) ÷ i.

Here, PMT is the deposit per period, i is the periodic rate and m is the number of deposits. A beginning-of-period contribution earns one additional period of growth, so the ordinary-annuity result is multiplied by (1 + i).

Increasing contributions over time

A fixed monthly contribution can lose purchasing power when prices and income change. The calculator can increase the contribution by a selected percentage each year. For example, a contribution of 250 with 5% annual growth becomes 262.50 in year two and 275.63 in year three.

This option can model contributions that rise with income, but later payments must remain affordable.

One-time deposits and withdrawals

Many real plans include a bonus, inheritance, tuition payment, home deposit or emergency withdrawal. Each extra cash flow has a year offset, a month offset and an amount. Positive values add money; negative values remove it.

A withdrawal reduces the balance available for future compounding. The long-term cost therefore exceeds the amount withdrawn because the removed money also loses future growth. The calculator prevents withdrawals from taking the simulated balance below zero and displays a warning if the account becomes depleted.

Fees and their long-term effect

FINRA recommends including investment fees when calculating returns. A percentage fee may look small, but it reduces the balance that remains available to compound. The calculator supports:

• an initial one-time fee;
• an annual percentage fee deducted from the running balance;
• a fixed annual fee prorated through the year.

Consider two otherwise identical scenarios before choosing a product. A higher gross return does not always produce the better net result when it also carries higher ongoing costs.

Simplified tax estimates

The calculator can show no tax, annual tax on positive interest or tax on positive interest at the end of the term. These are planning conventions, not a complete tax engine.

Actual treatment may depend on account type, realised gains, allowances, withholding, losses and residence. Tax paid each year no longer earns future returns.

Use a qualified local source when tax materially affects a decision. The calculator’s tax result should be labelled as an estimate.

Inflation and purchasing power

The European Central Bank explains that inflation is a broad increase in prices that reduces how much a unit of currency can buy. A future balance can rise in nominal terms while delivering much less purchasing power.

The calculator estimates real value with:

Real value = nominal balance ÷ (1 + inflation rate)^years.

A constant inflation assumption simplifies reality. Actual inflation changes over time and differs across households because spending patterns differ.

Financial goal planner

The goal mode can solve for one of three variables while keeping the other assumptions unchanged:

• the required regular contribution;
• the required annual rate;
• the required time to reach the target.

Fees, taxes, growing contributions and dated withdrawals complicate closed-form formulas, so the calculator uses numerical search with the full simulation.

A required return is not a recommendation. If the result demands an unusually high rate, the safer planning response may be a longer term, a lower target or larger contributions rather than assuming greater investment risk.

Scenario comparison

Comparison mode can evaluate several combinations of principal, contribution, return and percentage fee under the same duration, tax, inflation and cash-flow assumptions.

A fair comparison should disclose costs, liquidity, risk, guarantees, tax treatment and possible loss of principal. FINRA’s communication rules emphasise these differences.

The largest projected balance is not automatically the best choice. A lower-return insured deposit and a higher-return market investment do not have the same risk, access or protection.

Rule of 72 and exact doubling time

The Rule of 72 gives a quick estimate:

Approximate doubling time = 72 ÷ annual return in percent.

At 6%, the estimate is 12 years. The exact formula using an effective annual rate is:

Exact doubling time = ln(2) ÷ ln(1 + effective annual rate).

At an effective rate of 6%, the exact result is about 11.90 years. Both methods ignore fees, taxes, deposits and withdrawals.

How to choose realistic assumptions

1. Identify whether the stated rate is nominal or effective.
2. Copy the actual compounding frequency from the product terms.
3. Separate gross return, account fee and fund expense.
4. Use a contribution amount that remains affordable.
5. Record one-time cash flows rather than hiding them in the starting balance.
6. Use a documented inflation assumption.
7. Run conservative, central and optimistic scenarios.
8. Review the plan when rates, fees, income or goals change.

Investor.gov warns that investments do not guarantee profits, so a forecast should show several assumptions rather than one certain-looking return.

Common mistakes

• entering a percentage as 6 instead of 0.06 in a manual formula;
• compounding an effective annual rate again;
• placing end-of-period deposits at the beginning;
• ignoring fees because they appear small;
• treating taxes as identical in every country;
• comparing nominal balances while ignoring inflation;
• assuming a constant market return every year;
• counting withdrawals as though they continued to earn interest;
• using the Rule of 72 for a negative or zero return;
• treating a calculator result as financial advice.

Frequently asked questions

Official sources

• Investor.gov: What is compound interest?
• Investor.gov: Compound Interest Calculator
• Consumer Financial Protection Bureau: How compound interest works
• CFPB: Annual percentage yield formula and disclosure rules
• FINRA: Calculating investment returns and costs
• European Central Bank: What is inflation?
• Investor.gov: Introduction to investing and risk

Sources reviewed: 21 June 2026.