What are the assumptions of the Compound Interest formula?

The interest rate is constant. Real rates change with market conditions. All interest is reinvested (not withdrawn). Withdrawals reduce compounding. No additional contributions. For recurring deposits, the formula becomes a series of compounding events. No taxes on the interest. Tax-advantaged accounts (401k, IRA) defer or eliminate this. No fees or expense ratios. Real accounts charge 0.04%–1.5% annually, which compounds over decades. The full compounding period is used. Some accounts compound only on the minimum balance or specific dates.

What are the limitations of Compound Interest?

Real returns are usually lower than nominal returns due to inflation. Use the inflation calculator to see the real value. Investment returns are not constant. The model assumes a fixed rate; actual investments fluctuate. Tax drag (capital gains, dividends) reduces actual compounded growth. Sequence-of-returns risk matters: a downturn early in retirement can permanently impair a portfolio even with the same average return. Currency inflation in some countries (e.g. Argentina, Turkey) makes nominal returns meaningless without real-value adjustment. This calculator does not model dividend reinvestment separately — it assumes a single blended return rate. The Rule of 72 is a quick estimate: precise doubling time is ln(2) / ln(1 + r), which gives 9.01 years at 8% vs the Rule's 9.0 years — close but not exact. APY (Annual Percentage Yield) and APR (Annual Percentage Rate) differ: APY includes compounding, APR is the nominal rate. For savings, compare APY; for loans, compare APR. For retirement planning, the 4% rule (safe withdrawal rate) assumes a 30-year horizon, 50/50 or 60/40 stock/bond allocation, and US historical returns — it may not apply in low-return decades.

Methodology

How we calculate compound interest

Our methodology for the Compound Interest calculator: the formula, step-by-step calculation, authoritative sources, and limitations. Reviewed quarterly.

Formula

A = P(1 + r/n)^(nt)

Step-by-step

1
Identify the principal (P): the initial deposit or investment.
2
Identify the annual interest rate (r) as a decimal (5% → 0.05).
3
Identify the compounding frequency (n): annually = 1, quarterly = 4, monthly = 12, daily = 365.
4
Identify the time in years (t).
5
Compute (1 + r/n): the per-period growth rate.
6
Raise that to the power n×t: the total number of compounding periods.
7
Multiply by P: that is the future value (A). Subtract P to get interest earned.
8
For monthly contributions, add a second term: PMT × [((1 + r/n)^(n×t) − 1) / (r/n)]. Total = lump sum + contributions.
9
Compare APY vs APR: APY = (1 + r/n)^n − 1, which is the true annual yield including compounding.

Authoritative sources

Every claim on this page is backed by an authoritative source.

Assumptions

What we take to be true when applying this formula.

The interest rate is constant. Real rates change with market conditions.
All interest is reinvested (not withdrawn). Withdrawals reduce compounding.
No additional contributions. For recurring deposits, the formula becomes a series of compounding events.
No taxes on the interest. Tax-advantaged accounts (401k, IRA) defer or eliminate this.
No fees or expense ratios. Real accounts charge 0.04%–1.5% annually, which compounds over decades.
The full compounding period is used. Some accounts compound only on the minimum balance or specific dates.

Limitations

What this method does NOT capture.

Real returns are usually lower than nominal returns due to inflation. Use the inflation calculator to see the real value.
Investment returns are not constant. The model assumes a fixed rate; actual investments fluctuate.
Tax drag (capital gains, dividends) reduces actual compounded growth.
Sequence-of-returns risk matters: a downturn early in retirement can permanently impair a portfolio even with the same average return.
Currency inflation in some countries (e.g. Argentina, Turkey) makes nominal returns meaningless without real-value adjustment.
This calculator does not model dividend reinvestment separately — it assumes a single blended return rate.
The Rule of 72 is a quick estimate: precise doubling time is ln(2) / ln(1 + r), which gives 9.01 years at 8% vs the Rule's 9.0 years — close but not exact.
APY (Annual Percentage Yield) and APR (Annual Percentage Rate) differ: APY includes compounding, APR is the nominal rate. For savings, compare APY; for loans, compare APR.
For retirement planning, the 4% rule (safe withdrawal rate) assumes a 30-year horizon, 50/50 or 60/40 stock/bond allocation, and US historical returns — it may not apply in low-return decades.

Editorial note

Reviewed against SEC investor education and Investopedia methodology. Covers lump-sum, contributions, APY vs APR, sequence-of-returns risk, currency inflation, and Rule of 72 precision.

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Last reviewed: 2026-06-15 • Reviewed by: CalcxApp editorial team