Compound Frequency and EAR: Turning Nominal into Real Returns
Compounding frequency transforms the nominal rate into what you actually earn: the effective annual rate (EAR). The higher the frequency, the higher the EAR—though gains taper at typical market rates.
Key takeaways
- EAR converts nominal rate + frequency into a comparable annual metric.
- Daily vs monthly differences are modest at typical rates; savings rate dominates.
- Compare EARs across products (HYSAs, CDs, funds) to avoid apples vs oranges.
Key formulas
- Future value: A = P(1 + r/n)^(n·t)
- EAR: (1 + r/n)^n − 1
Practical takeaways
- Daily vs monthly compounding differences are modest below ~10% annual rates
- Over long horizons, frequency differences accumulate but remain secondary to contribution rate
- Focus first on savings rate and fees; then optimize compounding frequency
Step-by-step: compare products via EAR
- Gather nominal rate and compounding frequency for each product.
- Compute EAR for each; rank by EAR after fees.
- Consider liquidity/penalties (CDs vs HYSAs) alongside EAR.
Worked example
- HYSA 4.80% daily → EAR ≈ 4.92%
- CD 5.10% monthly → EAR ≈ 5.22% (but early withdrawal penalty risk)
Common pitfalls
- Comparing nominal rates with different frequencies
- Ignoring account fees or penalties that reduce realized return
- Chasing frequency while neglecting contribution rate
Quick checklist
- EARs computed and compared
- Liquidity needs assessed
- Fees/taxes considered
Decision matrix: when frequency matters
- Short horizon (<1y), low rates (<4%): frequency effect negligible → prioritize liquidity and fees.
- Medium horizon (1–5y), moderate rates (4–7%): minor but visible difference → choose higher frequency if costs equal.
- Long horizon (5y+), higher rates (7–10%): difference accumulates → higher frequency more valuable; still second to contribution rate.
Case study A: emergency fund vs CD
- 3-month expenses in HYSA (daily, 4.7% APY); surplus in 12m CD (monthly, 5.1% nominal) → EAR advantage for CD, but penalty risk argues for split allocation.
Case study B: retirement contributions
- 401(k) biweekly contributions vs monthly contributions at same fund
- Result: timing differences are small compared to contribution rate; use automation aligned with pay cycle.
FAQ (extended)
Is APY always comparable across banks? APY is standardized for deposits, but confirm compounding basis and any fees.
Do funds report EAR? Investment funds disclose annualized returns; compounding is embedded. Compare net-of-fee annualized figures.
What about inflation? Compare real return ≈ EAR − inflation to assess purchasing power.
Try it now
- Open Investment & Compound Calculator
- Toggle between yearly/quarterly/monthly/daily
- Compare final balances and EAR side-by-side
Deeper math intuition
Increasing compounding frequency raises the number of times interest is added to principal. At common rates, the incremental gain from monthly→daily is small because the term (r/n) becomes tiny as n rises.
Continuous compounding (for intuition only)
EAR ≈ e^r − 1 when compounding is continuous. For r = 0.08, EAR ≈ 8.33%. Daily vs continuous differs by basis points—illustrating diminishing returns from ever-higher frequencies.
Benchmark differences (illustrative)
- 4% nominal: annual EAR 4.00%; monthly EAR ≈ 4.07%; daily EAR ≈ 4.08%
- 8% nominal: annual 8.00%; monthly ≈ 8.30%; daily ≈ 8.33%
- 12% nominal: annual 12.00%; monthly ≈ 12.68%; daily ≈ 12.75%
Myths vs reality
- “Daily compounding doubles my returns.” → Myth. Frequency boosts EAR modestly at normal rates; contribution rate dominates.
- “APY always includes fees.” → Myth. APY standardizes compounding, not account fees; compare net-of-fee yields.
- “More frequent is always better for all goals.” → Myth. Liquidity and penalties can outweigh tiny EAR gains.
Case study C: laddered CDs vs single HYSA
- CDs: 6/12/18/24 months at quoted nominal rates with monthly compounding; HYSA daily compounding.
- Result: ladder can raise EAR modestly and manage reinvestment risk; HYSA keeps liquidity. Split capital based on emergency horizon.
Case study D: auto-contributions timing
- Biweekly vs monthly contributions to the same index fund.
- Outcome: small timing benefit to biweekly, swamped by contribution rate and market variance; choose cadence that maximizes consistency.
FAQs
Does frequency matter for stock funds? Mutual funds/ETFs report annualized returns; compounding is embedded. Focus on fees and time in market.
Is APY comparable across countries? APY definitions can vary; when in doubt, compute EAR from the stated nominal+frequency yourself.
Should I chase daily over monthly in savings? Only if all else is equal. A higher nominal with monthly compounding can beat a lower daily APY.
Glossary
- APY: annual percentage yield; standardized deposit return including compounding.
- EAR: effective annual rate; converts nominal+frequency into a comparable annual rate.
- Nominal rate: stated annual rate before compounding.
- Compounding frequency: how often interest is added to principal.
Extended worked example (side-by-side)
Assume ¥100,000 for 5 years at 7.2% nominal.
- Annual: A = 100,000·(1+0.072)^5 ≈ 141,641 (EAR 7.20%)
- Monthly: A = 100,000·(1+0.072/12)^(12·5) ≈ 142,154 (EAR ≈ 7.46%)
- Daily: A ≈ 142,244 (EAR ≈ 7.49%)
Incremental lift: monthly vs annual ≈ 513; daily vs monthly ≈ 90. The bigger driver of outcomes is contribution rate and time horizon—not squeezing from monthly to daily.
Budget allocation examples
- Short-term cash (taxes in 4–6 months): prioritize liquidity; HYSA (daily) beats a CD if penalties would apply.
- Medium-term goal (car in 18 months): compare CD ladder EAR vs HYSA APY; small EAR gains may be worth partial lockups.
- Long-term investing (10y+): frequency is embedded in total-return numbers; fees and savings rate dominate.
FAQs (extended)
Is APY affected by leap years? Banks standardize on 365/360 conventions; the difference is immaterial for most savers.
Do brokered CDs compound monthly? Many credit interest monthly but pay at maturity; compute EAR from terms provided.
Can frequency change midterm? Variable-rate accounts can change nominal rate; frequency conventions typically remain constant per product.
Rules of thumb
- If rates are low and horizon is short, frequency barely matters—prioritize liquidity and fees.
- For multi‑year horizons, monthly vs daily adds basis points, not percentage points; contribution rate and fees dominate.
- Always compare EAR or APY across products; avoid mixing nominal rates with different compounding bases.