Simple mental math vs. logarithmic precision
Account illustrations use the capital below. Deposits add new capital; pure-growth doubling stays separate.
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The Rule of 72 estimates how long it takes to double your money: divide 72 by the annual return rate. At 8% returns, your money doubles in 72/8 = 9 years. At 6%, it takes 12 years. This quick mental math works best for rates between 4-12%.
Doubling Time ≈ 72 ÷ Annual Return Rate 72/r is a mental approximation with r expressed in percent.
Select whether you want to calculate Time to Double, the Required Rate for a goal, or the time needed to reach a specific Target Balance.
Start with a nominal annual rate and compounding frequency. Compare approximate and exact times, then open the account planner to include capital and month-end deposits.
Select a chart point to inspect its approximation error. Use Goal or Required Rate for funded targets; review the link before sharing financial assumptions.
Doubling Time ≈ 72 ÷ Annual Return Rate R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim.
t = ln(2) / [n × ln(1 + R/(100n))] R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim.
q = (1 + R/(100n))^(n/12); B_m = B_(m−1) × q + M Interpolation convention: a nominal quote compounded n times/year is converted to equal monthly growth. Deposits occur at each month end. Tax is an illustrative charge on positive period gains; it is not buy-and-hold capital-gains taxation. Rate and Goal modes use nominal dollars without the Double panel's tax/inflation toggles. Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable. Charts and exported monthly ledgers are capped at 100 displayed years.
Author: Quinn Sumner - Editor
Owner: Quinn Sumner - Editorial owner
Reviewer: Calculover Editorial Review - Source and limitation review
Last reviewed: 2026-05-10
Last verified: 2026-05-10
Data effective: 2026-05-10
R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim. Interpolation convention: a nominal quote compounded n times/year is converted to equal monthly growth. Deposits occur at each month end. Tax is an illustrative charge on positive period gains; it is not buy-and-hold capital-gains taxation. Rate and Goal modes use nominal dollars without the Double panel's tax/inflation toggles.
Assumption: Rule of 72 relies on the values the user enters and does not independently verify income, balances, legal status, policy terms, or market quotes.
Assumption: Interpolation convention: a nominal quote compounded n times/year is converted to equal monthly growth. Deposits occur at each month end. Tax is an illustrative charge on positive period gains; it is not buy-and-hold capital-gains taxation. Rate and Goal modes use nominal dollars without the Double panel's tax/inflation toggles.
Assumption: Actual market returns are volatile and can differ materially from the constant-rate or scenario assumptions.
Rule of 72 does not recommend securities, predict returns, include every fee or tax consequence, or assess whether an investment is suitable for the user.
Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable. Charts and exported monthly ledgers are capped at 100 displayed years.
This calculator is for educational and illustrative purposes only. It does not constitute financial advice. Actual investment returns vary and are not guaranteed. Tax treatment depends on your individual circumstances — consult a licensed financial advisor or CPA before making investment decisions.
Professional guidance: Rule of 72 is for investment math education only and is not investment, tax, legal, or financial advice. Consider risk, fees, taxes, and suitability before acting.
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Hypothetical fixed-rate account
Hypothetical 10% nominal annual quote, monthly compounding, no deposits:72/10=7.2 years; exact doubling 6.9603129917 years.$10,000 reaches $20,000 in this constant-rate model, without a market-return guarantee.
Hypothetical fixed-rate account
Nominal 4.5% compounded monthly gives 4.5939825041% effective annually. With 3% annual inflation, real growth is 1.5475558292%; exact real doubling 45.1354878149 years, without deposits or taxes.
Inflation Halving Purchasing Power
At 3% constant inflation, exact purchasing-power halving takes 23.4497722504 years;72/3=24 years is approximate. After 24 years,$100,000 without returns buys $49,193.37 at starting prices.
Use either format to cite this calculator in a paper, report, or resource list.
72/r is a mental approximation with r expressed in percent. Exact pure growth uses the selected compounding. Deposits are new capital, not investment returns. Tax drag applies to positive compounding-period gains only; inflation deflates the resulting nominal account. No market-performance or attainability guarantee is implied.
R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim.
For continuous compounding at annual percentage rate R, doubling time is 100×ln(2)/R, approximately 69.3147/R. The constant 69.3 is rounded. It is a different quote convention from the selected discrete compounding.
Interpolation convention: a nominal quote compounded n times/year is converted to equal monthly growth. Deposits occur at each month end. Tax is an illustrative charge on positive period gains; it is not buy-and-hold capital-gains taxation. Rate and Goal modes use nominal dollars without the Double panel's tax/inflation toggles.
Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable. Charts and exported monthly ledgers are capped at 100 displayed years.
Deposits enter at each month end and add new capital.
Matched monthly funding: nominal account, deposits and a separate simple-interest arithmetic reference
Matched cash flows at the same selected compounding and adjustments
72/r is a mental approximation with r expressed in percent. Exact pure growth uses the selected compounding. Deposits are new capital, not investment returns. Tax drag applies to positive compounding-period gains only; inflation deflates the resulting nominal account. No market-performance or attainability guarantee is implied.
Nominal and inflation rates must use the same annual basis. Compute the exact ratio rather than subtracting rates. The optional tax model reduces only positive returns before this ratio.
Interpolation convention: a nominal quote compounded n times/year is converted to equal monthly growth. Deposits occur at each month end. Tax is an illustrative charge on positive period gains; it is not buy-and-hold capital-gains taxation. Rate and Goal modes use nominal dollars without the Double panel's tax/inflation toggles.
Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable. Charts and exported monthly ledgers are capped at 100 displayed years.
Editable hypothetical return quotes; matching deposits, compounding, tax and inflation, not observed historical returns
72/r is a mental approximation with r expressed in percent. Exact pure growth uses the selected compounding. Deposits are new capital, not investment returns. Tax drag applies to positive compounding-period gains only; inflation deflates the resulting nominal account.
R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim.
At constant 3% inflation, exact purchasing-power halving is 23.4497722504 years;72/3=24 years is approximate. After 24 years,$100,000 of non-earning cash has $49,193.37 of starting purchasing power. This illustrates a price ratio, not a falling-target funding solver.
R is the nominal annual percentage quote and n is periods per year. Without adjustments, exact pure-growth time is ln(2)/(n×ln(1+R/(100n)));72/R is separate. The difference depends on rate and compounding and is displayed numerically, without a universal accuracy claim.
Illustrative tax applies only to positive period gains; no loss credit or account-specific tax rule is assumed.
For continuous compounding at annual percentage rate R, doubling time is 100×ln(2)/R, approximately 69.3147/R. The constant 69.3 is rounded. It is a different quote convention from the selected discrete compounding.
Editable hypothetical return quotes; matching deposits, compounding, tax and inflation, not observed historical returns
Matched monthly funding: nominal account, deposits and a separate simple-interest arithmetic reference Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable. Charts and exported monthly ledgers are capped at 100 displayed years.
Enter a nominal annual return quote and choose its compounding frequency. Deposits enter at each month end and add new capital. Contribution targets are checked through 12,000 monthly deposits (1,000 years); unachieved targets stay unavailable.
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