Calculate compound interest across 8 frequencies (Daily, Monthly, Continuous). Convert APR to APY, compare simple vs compound growth, and solve the Rule of 72.
Converted from 6% Monthly (12/yr)
To achieve the same yield as a 6.00% Monthly (12/yr) rate, a Annual (1/yr) rate requires 6.1678% (0.1678% higher).
Exact equivalent nominal rates required across 8 compounding frequencies to yield equal effective returns.
| Compounding Frequency | Equivalent Rate (%) | Effective Annual Yield (APY %) | Difference vs Annual (%) |
|---|---|---|---|
| Daily (365/yr) | 5.98554% | 6.16778% | -0.18224% |
| Weekly (52/yr) | 5.98850% | 6.16778% | -0.17929% |
| Bi-Weekly (26/yr) | 5.99194% | 6.16778% | -0.17584% |
| Monthly (12/yr) | 6.00000% | 6.16778% | -0.16778% |
| Quarterly (4/yr) | 6.03005% | 6.16778% | -0.13773% |
| Semi-Annual (2/yr) | 6.07550% | 6.16778% | -0.09228% |
| Annual (1/yr)Selected Target | 6.16778% | 6.16778% | 0.00000% |
| Continuous | 5.98505% | 6.16778% | -0.18273% |
| Compounding Schedule | Future Value ($) | Total Interest Earned ($) | Effective Yield (%) |
|---|---|---|---|
| Annual (1/yr) | $19,671.51 | +$9,671.51 | 7.0000% |
| Semi-Annual (2/yr) | $19,897.89 | +$9,897.89 | 7.1200% |
| Quarterly (4/yr) | $20,015.97 | +$10,015.97 | 7.1900% |
| Monthly (12/yr) | $20,096.61 | +$10,096.61 | 7.2300% |
| Bi-Weekly (26/yr) | $20,118.59 | +$10,118.59 | 7.2400% |
| Weekly (52/yr) | $20,128.05 | +$10,128.05 | 7.2500% |
| Daily (365/yr) | $20,136.18 | +$10,136.18 | 7.2500% |
| ContinuousMaximum Yield | $20,137.53 | +$10,137.53 | 7.2500% |
The Rule of 72 is exceptionally accurate for interest rates between 5% and 10% (error is under 1%).
| Year | Simple Value | Compound Value | Interest Bonus |
|---|---|---|---|
| 1 Yrs | $10,800 | $10,830 | +$30 |
| 5 Yrs | $14,000 | $14,898.46 | +$898.46 |
| 10 Yrs | $18,000 | $22,196.4 | +$4,196.4 |
| 20 Yrs | $26,000 | $49,268.03 | +$23,268.03 |
| 30 Yrs | $34,000 | $109,357.3 | +$75,357.3 |
Compound interest occurs when previously accumulated interest is added back to the principal sum of a deposit or loan, allowing subsequent interest calculations to be based on an expanding foundation. Compound interest can accelerate long-term capital growth because previously accrued interest can itself earn additional returns.
When saving or investing, compounding operates in your favor. Reinvesting interest and dividends accelerates wealth accumulation over multi-decade horizons in cash deposit vehicles and diversified portfolios.
When borrowing money, compound interest increases the cost of carrying balances. If finance charges are added to unpaid principal or calculated daily, overall debt balances can escalate if payments are delayed.
For discrete compounding schedules (daily, monthly, quarterly, semi-annually, or annually), future value is computed using the standard compound interest formula:
When the nominal interest rate is zero ($r = 0$), the formula simplifies to:
Under a zero-percent rate assumption, total interest earned is identically $0.00, and the ending balance equals the original principal deposit. To project single lump sums under various discount rate and duration assumptions, use our future value calculator.
To illustrate discrete compounding mechanics, let us evaluate the mathematical model under a hypothetical scenario:
The compounding frequency (n) specifies how often accrued interest is credited back to the principal balance during the year. Under identical starting principal (P = $10,000), annual nominal rate (r = 7.0%), and time horizon (t = 10 Years), more frequent compounding yields higher final balances due to earlier reinvestment of intermediate returns:
| Compounding Schedule | Periods / Year (n) | Final Balance (A) | Total Interest Earned | Effective Annual Yield (APY) |
|---|---|---|---|---|
| Annual | 1 | $19,671.51 | $9,671.51 | 7.0000% |
| Semi-Annual | 2 | $19,897.89 | $9,897.89 | 7.1225% |
| Quarterly | 4 | $20,015.97 | $10,015.97 | 7.1859% |
| Monthly | 12 | $20,096.61 | $10,096.61 | 7.2290% |
| Bi-Weekly | 26 | $20,118.59 | $10,118.59 | 7.2386% |
| Weekly | 52 | $20,128.05 | $10,128.05 | 7.2458% |
| Daily | 365 | $20,136.18 | $10,136.18 | 7.2501% |
| Continuous | ∞ | $20,137.53 | $10,137.53 | 7.2508% |
Under the stated assumptions, increasing compounding frequency from Annual to Monthly produces an extra +$425.10 in interest. Increasing from Daily to Continuous adds only +$1.35 over 10 years, demonstrating asymptotic diminishing returns.
Financial institutions utilize distinct interest rate metrics depending on whether products involve borrowing or depositing funds:
The stated annual percentage rate before intra-year compounding is applied. In this calculator, APR is treated as a nominal rate ($r$) for mathematical compounding comparisons. Official consumer APR disclosures on loans under the Truth in Lending Act (TILA) may incorporate additional finance charges or origination fees.
The standardized effective annual rate reflecting intra-year compounding over a 365-day year:
Under the US Truth in Savings Act (TISA), banks disclose APY on deposit products so consumers can compare accounts with differing compounding schedules.
For a fixed nominal interest rate, continuous compounding represents the mathematical limiting value of increasingly frequent discrete compounding as $n$ approaches infinity.
Hypothetical model: $5,000 at 6.5% over 5 years yields $6,920.15 (+$1,920.15 interest, 1.3840x multiplier).
Estimates doubling time via $T \approx 72 / r$. For an 8% return, Rule of 72 estimates 9.00 years vs. exact logarithmic doubling of 9.01 years (0.07% error).
The Rule of 69.3 ($69.3 / r$) provides closer estimates for continuous compounding or rates under 5%.
Simple interest calculates returns strictly on the initial deposit ($A = P(1+rt)$), whereas compound interest reinvests earnings ($A = P(1+r/12)^(12×t)$):
| Milestone ($10,000 at 8% Annual Rate) | Simple Interest Balance | Compound Balance (Monthly) | Compounding Advantage (Bonus) |
|---|---|---|---|
| Year 1 | $10,800.00 | $10,830.00 | +$30.00 |
| Year 5 | $14,000.00 | $14,898.46 | +$898.46 |
| Year 10 | $18,000.00 | $22,196.40 | +$4,196.40 |
| Year 20 | $26,000.00 | $49,268.03 | +$23,268.03 |
| Year 30 | $34,000.00 | $109,357.30 | +$75,357.30 |
Commercial bank products differ in APY, compounding conventions, minimum balances, and early-withdrawal penalties. To model term deposit growth, evaluate our CD calculator or plan cash reserves with our savings calculator.
Credit-card interest calculations depend on the issuer and cardholder agreement. Many U.S. issuers use daily periodic rates or average-daily-balance methods. To estimate payoff timelines, use our credit card payoff calculator.
Consider an illustrative investor contributing $300/month for 40 years under a constant 8.0% annual return assumption compounded monthly:
*Assumed modeling parameter only; past performance does not guarantee future results. For retirement planning, explore our retirement calculator and SIP calculator.
At a 0.0% fee, the balance grows to $761,225.50. After a 1.0% annual management fee (6.0% net return), the balance reaches $574,349.12, representing a cumulative fee drag of $186,876.38.
Compound interest is the interest calculated on the initial principal plus all accumulated interest from prior periods, allowing savings and investments to grow exponentially over time.
The standard formula is A = P × (1 + r/n)^(n×t), where A is future value, P is principal, r is nominal annual interest rate as a decimal, n is compounding frequency per year, and t is years.
In this calculator, APR is treated as the stated nominal annual rate before intra-year compounding, while APY (Annual Percentage Yield) reflects the effective annual return earned when intra-year compounding is included. Official consumer APR disclosures on loans may incorporate additional upfront fees and finance charges.
More frequent compounding (such as daily or monthly) reinvests earnings earlier, producing higher effective annual yields and larger final balances compared to annual compounding under the same nominal rate.
Effective Annual Rate (EAR) is the standardized annualized rate that accounts for compounding within the year (EAR = (1 + r/n)^n - 1), allowing direct comparisons between financial products with differing compounding schedules.
Continuous compounding represents the mathematical upper bound of compounding where interest is calculated and added constantly at every infinitely small instant using the formula A = P × e^(rt).
The Rule of 72 is a mental shortcut to estimate doubling time by dividing 72 by the annual interest rate (72 / r). It is accurate within 1% error for interest rates between 5% and 10%.
Simple interest calculates returns strictly on original principal (A = P × (1 + rt)), resulting in linear growth, whereas compound interest generates accelerating exponential growth.
Yes. When unpaid interest on revolving credit lines or loans is added back to the principal or calculated on a daily periodic basis, finance charges expand if balances are not paid off promptly.
Yes. All computations execute 100% client-side in your web browser. No financial data, interest rates, or balances are transmitted to external servers.
All computations execute 100% client-side in your web browser using standard IEEE 754 floating-point equations. No financial inputs, interest rates, or balances are stored or transmitted to external servers. This calculator is provided for educational and mathematical scenario modeling only and does not constitute financial advice, banking recommendations, or a guarantee of investment returns. Past historical performance does not guarantee future results.