Compound Interest Calculator

The Compound Interest Calculator below converts and compares nominal APR and effective APY yields across diverse global compounding periods. Please use our Interest Calculator to calculate total interest earnings and investment growth schedules.

Input Interest Compound Equals Output Interest Compound
%
6.16778%
A nominal interest rate of 6.000% compounded Monthly (APR) is mathematically equivalent to 6.16778% compounded Annually (APY), producing an effective annual yield (APY) of 6.16778%.
Quick Presets:
Compounding Period Equivalence Matrix ($10,000 Initial Principal)
Compounding Frequency Periods/Yr Equivalent Nominal APR Periodic Rate 1-Yr Balance 5-Yr Balance 10-Yr Balance 20-Yr Balance
Portfolio Growth Over 20 Years (Compound Yield Trajectory) Constant yield projection
Compounding Frequency Impact at Unadjusted Nominal Rate
Compounding Frequency Periods/Yr Nominal Rate (Stated APR) Effective Yield (APY) 10-Yr Balance ($10k Deposit) 10-Yr Total Interest

What is Interest?

Interest represents the fundamental cost of borrowed capital or the financial return generated by depositors and lenders. It is expressed as an annualized percentage rate against the initial principal balance. When consumers take out mortgages or auto loans, lenders charge interest over the repayment term. In contrast, when savers deposit money into high-yield accounts, financial institutions pay interest for the temporary use of those funds.

Simple Interest vs. Compound Interest

Simple interest accrues exclusively on the original principal balance, yielding a fixed, linear payout throughout each cycle. Compound interest, by contrast, reinvests accumulated earnings back into the balance, calculating returns on both principal and prior interest. This compounding cycle fuels exponential portfolio growth over time, enabling long-term retirement investments and compound savings to outpace inflation and simple interest.

APR vs. APY: Compounding Frequencies Explained

Annual Percentage Rate (APR) denotes the nominal contractual rate excluding compounding effects, commonly quoted on consumer debt. Annual Percentage Yield (APY), or Effective Annual Rate (EAR), captures the true annualized return by incorporating compounding frequency. More frequent cycles—such as daily or monthly compounding—consistently produce an APY higher than the stated APR. This tool enables global investors and borrowers to evaluate competing bank terms on an equal footing.

Compounding Conversion Formulas

To convert an Annual Percentage Rate (APR) with compounding frequency n into an Effective Annual Yield (APY or EAR):

EAR = (1 + r / n)n - 1

Where:
• r = Stated annual nominal interest rate (decimal)
• n = Number of compounding intervals per calendar year
• EAR = Effective Annual Rate (yield including compounding)

To determine the equivalent nominal rate (rm) for any target compounding period m:

rm = m × [(1 + EAR)(1 / m) - 1]

For continuous compounding:
EAR = er - 1    |    rcontinuous = ln(1 + EAR)

The Rule of 72 & Practical Applications

The Rule of 72 provides a rapid mathematical heuristic to estimate how many years an asset needs to double under compounding returns. Dividing 72 by the annual compounding rate delivers a reliable approximation of portfolio doubling velocity. For instance, an investment compounding at 6% APY doubles in roughly 12 years (72 / 6 = 12). This benchmark assists financial planners worldwide in evaluating wealth milestones and long-term targets.