How is the final amount calculated with compound interest?

The final amount is A = P × (1 + r/n)^(n×t). With regular contributions C at the end of each period the contribution term C × [((1 + r/n)^(n×t) − 1) / (r/n)] is added. P is the principal, r the annual rate (decimal), n periods per year, t years.

Does compounding frequency matter?

Yes — more frequent compounding (monthly, daily) yields a slightly higher effective return for the same nominal annual rate. Continuous compounding is the theoretical limit: A = P × e^(r×t).

Does this calculator adjust for taxes or inflation?

No. The calculator shows nominal growth before taxes and inflation. For real purchasing power, adjust results by expected inflation or model after-tax returns.

Compound Interest Calculator - AkCalculators.com

Q: Are contributions assumed at the start or end of period?

This calculator assumes contributions are made at the end of each compounding period (ordinary annuity). To model beginning-of-period contributions (annuity due), multiply the contribution term by (1 + r/n).

Q: What is the Rule of 72?

A quick estimate to find doubling time: divide 72 by the annual interest rate (in percent). For example, at 6% annual interest, doubling time ≈ 72 / 6 = 12 years.

📈 Compound Interest Calculator

Compute final amount, total contributions, and interest earned with compound interest. Supports periodic contributions and multiple compounding frequencies. Includes a year-by-year growth table and a full guide on compound interest and long-term saving strategies.

Compound Interest Tool

Initial principal

Annual interest rate (%)

Times compounded per year

Years

Regular contribution per period (optional; applied at end of each period)

Introduction

Compound interest is one of the most powerful forces in personal finance. Described by Einstein (apocryphally) as the “eighth wonder of the world,” compound interest makes your money grow faster than simple interest because interest earns interest. Whether you’re saving for retirement, building an emergency fund, or estimating investment growth, understanding compound interest — the variables that drive it and the strategies to harness it — is essential. This guide explains the math, demonstrates examples, explores compounding frequencies (annual, monthly, daily, and continuous), explains the Rule of 72, and offers practical advice for everyday savers.

What is compound interest?

Compound interest occurs when interest earned on a balance is reinvested so future interest is earned on the interest as well as the original principal. In contrast to simple interest — where interest is computed only on the principal — compound interest accelerates growth because each period's interest becomes part of the base earning interest in the next period.

The basic formula

The classic formula for compound interest without periodic contributions is:

Final amount	`A = P × (1 + r/n)^(n×t)`
Where	P = principal, r = annual interest rate (decimal), n = number of compounding periods per year, t = years.

If you add a regular contribution of amount C at the end of every compounding period, the final amount becomes:

With contributions	`A = P × (1 + r/n)^(n×t) + C × [ ( (1 + r/n)^(n×t) − 1 ) / (r/n) ]`
Notes	This assumes contributions are made at the end of each period. If contributions are at the beginning (annuity due), multiply the contribution term by (1 + r/n).

Difference between simple and compound interest

Simple interest accumulates based on the original principal only; compound interest builds on previously earned interest. For short periods or low rates the difference may be small, but over long horizons (decades), compound interest can produce vastly larger amounts because of exponential growth.

Compounding frequency: annual, monthly, daily, continuous

Compounding frequency affects how often interest is added to the balance. For the same nominal annual rate, more frequent compounding produces a higher effective annual yield because interest is applied more often. Common frequencies:

Annually (n=1) — interest added once per year.
Monthly (n=12) — interest added monthly (common for savings and mortgages).
Daily (n=365) — interest added daily (some banks use daily compounding for savings).
Continuous compounding — the theoretical limit as n → ∞; formula: A = P × e^(r×t). Continuous compounding yields a slightly higher result than any finite periodic compounding at the same nominal rate.

The Rule of 72

The Rule of 72 is a quick mental trick to estimate how long it takes for an investment to double: divide 72 by the annual interest rate (in percent). For example, at 6% per year, doubling time ≈ 72 / 6 = 12 years. It's an approximation (most accurate for rates between 4% and 12%) but useful for quick comparisons.

Worked examples

Example 1 — No contributions: Start with P = 10,000 at 5% annual, compounded monthly (n=12) for 30 years. Using the formula A = P(1 + r/n)^(n×t), we get A ≈ 43,219. That growth is purely from compound interest.

Example 2 — With monthly contributions: Start with P = 10,000, contribute C = 200 every month, r = 5% annual, n = 12, t = 30. The contribution term dominates over time: final A ≈ P(1+r/n)^(360) + C × [ ((1+r/n)^(360) −1)/(r/n) ] → roughly 157,000 — contributions + compound interest combined produce a much larger result than interest alone.

The power of time and contributions

Time is the most powerful lever: small contributions over long periods compound dramatically. For example, saving 200 per month beginning at age 25 vs starting at 35 can produce a huge difference at retirement because of the extra decade of compound growth on both principal and interest.

Practical use cases

Retirement planning: Calculate how regular contributions grow into retirement savings and how changing contribution amounts affects final balance.
Education savings: Estimate future college costs using expected growth rates and planned contributions.
Debt growth: Compound interest also works against you — understand how unpaid balances grow when interest compounds.

Common mistakes & tips

Not matching compounding frequency when comparing rates — compare effective annual rates (EAR) rather than nominal rates.
Ignoring fees and taxes — gross growth may be reduced by taxes or account fees in real scenarios.
Assuming constant rates — real investments may vary; use conservative estimates for planning.
Procrastinating — starting early reduces the monthly amount you'd need to save for the same target.

Continuous compounding

Continuous compounding is a theoretical model useful for certain financial mathematics. It uses e (≈ 2.71828) and the formula A = P × e^(r×t). For practical banking and investing, discrete compounding (monthly or daily) is more common, but continuous compounding is a useful upper bound and simplifies some calculus-based models.

Putting it together — strategy suggestions

Start early — time multiplies the value of regular contributions.
Increase contributions gradually — even small raises applied to contributions help because they compound.
Prefer tax-advantaged accounts for long-term savings when possible (retirement accounts, tax-free growth, etc.).
Aim for higher real returns (after inflation) but be mindful of risk — diversification matters.

Conclusion

Compound interest is the engine behind long-term wealth building. It multiplies contributions and principal over time, and small regular contributions compounded consistently often outperform large lump sums made late. Use this calculator to test scenarios, try different compounding frequencies, and see how contributions and time influence final balances. Remember to factor in taxes, fees, and realistic return assumptions for practical planning.

FAQs

❓ Q: How is the final amount calculated?

💡 A: Final amount uses the compound interest formula: A = P × (1 + r/n)^(n×t). If you make a regular contribution C at the end of each period, add the term C × [((1 + r/n)^(n×t) − 1) / (r/n)].

❓ Q: What frequency should I use for compounding?

💡 A: Use the frequency your account or instrument uses — monthly for many savings accounts, daily for some bank accounts, etc. More frequent compounding gives slightly higher returns for the same nominal rate.

❓ Q: Does the calculator include inflation or taxes?

💡 A: No. This calculator shows nominal growth before taxes and without adjustment for inflation. To estimate real purchasing power, adjust results by expected inflation or model after-tax returns.

❓ Q: Are contributions assumed at the start or end of period?

💡 A: Contributions in this tool are assumed at the end of each compounding period (ordinary annuity). If you want beginning-of-period contributions (annuity due), the contribution term should be multiplied by (1 + r/n).

❓ Q: What is the Rule of 72?

💡 A: The Rule of 72 estimates doubling time: divide 72 by the annual interest rate (in percent). Example: at 6% annual, doubling time ≈ 72 / 6 = 12 years.

❓ Q: How can I use this for retirement planning?

💡 A: Enter expected starting balance, an estimated annual return, compounding frequency, the number of years until retirement, and planned regular contributions. The final amount gives a nominal projection — adjust for taxes and inflation for a realistic target.