Definition
Compounding is earning interest on interest. More frequent compounding increases the effective annual rate (APY) for a given APR.
Formula
APY = (1 + APR / n)^n - 1
Example
At 10% APR, annual compounding yields 10%. Monthly compounding yields 10.47% APY.
How to use it
- Compounding frequency (daily, monthly, quarterly) changes the effective return.
- APR is the nominal rate; APY reflects compounding effects.
- Small rate differences can compound into large gaps over long horizons.
- Compounding applies to growth rates too (revenue, users, and cash).
- Use the same compounding basis when comparing products.
- Long horizons amplify small compounding differences.
- Align compounding with payment timing when modeling loans or savings.
Common mistakes
- Comparing APR to APY without converting to the same basis.
- Assuming compounding frequency does not matter for short horizons.
- Ignoring fees that reduce effective yield.
- Mixing nominal and effective rates in the same model.
- Using annual rates in monthly models without converting.
- Applying compounding to one line item but not to the related assumptions.
Measured as
APY = (1 + APR / n)^n - 1
Misused when
- Comparing APR to APY without converting to the same basis.
- Assuming compounding frequency does not matter for short horizons.
- Ignoring fees that reduce effective yield.
- Mixing nominal and effective rates in the same model.
- Using annual rates in monthly models without converting.
- Applying compounding to one line item but not to the related assumptions.
Operator takeaway
- Compounding frequency (daily, monthly, quarterly) changes the effective return.
- APR is the nominal rate; APY reflects compounding effects.
- Small rate differences can compound into large gaps over long horizons.
- Tie Compounding to the same balance-sheet date, scenario, and decision memo you are using elsewhere in the model.
- Document which claims, costs, or adjustments your team includes before comparing numbers across forecasts, covenants, or valuation work.
Next decision
- Quantify the impact with APR to APY Calculator if you need to turn the definition into an operating assumption.
- Read APR vs APY: how compounding changes the effective rate if the decision depends on interpretation, policy, or trade-offs beyond the raw formula.
Where to use this on MetricKit
Calculators
- APR to APY Calculator: Convert APR to APY (and APY to APR) given compounding frequency.
Guides
- APR vs APY: how compounding changes the effective rate: A practical guide to APR vs APY: what each means, how to convert between them, and common comparison mistakes.