Overview
Interest accrual methods directly affect how much you pay on a loan or how much your investment grows over time. Lenders and account providers choose an accrual method (and compounding frequency) that determines the periodic rate applied to the outstanding balance. In my 15 years advising borrowers and savers, the single biggest blind spot I see is not converting different compounding frequencies to a common basis (effective annual rate or APY) before comparing offers.
How each method works — formulas and plain-English steps
Simple interest
- Formula: Interest = P × r × t
- P = principal, r = annual rate (decimal), t = time in years.
- How it behaves: Interest is computed only on the original principal and does not compound. Simple interest is common for short-term notes, auto title loans, and some business/promissory notes.
- Example: $2,000 at 10% simple interest for 2 years = 2,000 × 0.10 × 2 = $400 interest, total repayment $2,400.
Why it matters: If you’re comparing a short-term loan that uses simple interest to one that compounds, simple interest will usually cost less for the same nominal rate and term.
Compound interest (periodic compounding)
- Formula: A = P (1 + r/n)^(n t)
- A = amount after t years, n = compounding periods per year.
- Effective annual rate / APY: EAR = (1 + r/n)^n − 1. This converts nominal annual rate r and frequency n to a comparable annual return.
- How it behaves: Interest earned each period is added to the balance; subsequent periods earn interest on the larger balance (interest-on-interest).
- Examples:
- Annual compounding (n = 1): $10,000 at 6% for 10 years → A ≈ $10,000 × (1.06)^10 ≈ $17,908.50.
- Monthly compounding (n = 12): same nominal 6% → EAR = (1 + 0.06/12)^12 − 1 ≈ 6.17%.
Professional note: I often encourage clients to translate lender APRs into effective annual rates (EAR/APY) so they’re comparing like with like. Two loans with the same nominal APR can have different costs if one compounds monthly and the other daily.
Daily compounding and daily interest (credit cards and short-term debt)
- Daily periodic rate = APR / 365 (or 360, if the contract uses a 360-day year). The balance is updated daily using that periodic rate.
- Formula (daily compounding): A = P (1 + r/365)^(365 t)
- Example: $5,000 at 4% APR compounding daily for 1 year → A ≈ $5,000 × (1 + 0.04/365)^{365} ≈ $5,204 (≈4.08% effective).
Special note on credit cards: Many cards calculate interest on the card’s average daily balance using the daily periodic rate (APR/365). The Consumer Financial Protection Bureau (CFPB) explains how credit card interest accrues and encourages reviewing card agreements for calculation methods (CFPB). Always check the issuer’s periodic-rate method in your card’s terms (see CFPB resources).
Continuous compounding (theoretical maximum)
- Formula: A = P × e^(r t)
- Interpretation: Continuous compounding assumes compounding every instant. It’s rare in retail products but useful for modeling and understanding limits.
- Example: $10,000 at 6% for 10 years compounded continuously → A = 10,000 × e^{0.06×10} ≈ $18,221.
Comparing loans and investments: practical steps
- Identify the nominal rate and compounding frequency in the contract: annual, monthly, daily, or continuous.
- Convert to an effective annual rate (EAR/APY) using EAR = (1 + r/n)^n − 1. For daily compounding use n = 365 (or the contract’s base).
- Include mandatory fees when comparing cost. Fees can turn a lower-EAR offer into a more expensive one once amortized into the effective rate — see our piece on Understanding Effective APR for more detail.
- For installment loans (mortgages, auto loans), produce an amortization schedule to see how much of each payment is interest vs principal. The monthly payment formula for a fixed-rate installment loan is:
- M = P × (i (1 + i)^N) / ((1 + i)^N − 1)
- where i = monthly rate = APR/12 and N = total months.
- Use a spreadsheet or online calculator and always test different compounding frequencies and fee scenarios.
How accrual method affects different borrowers and products
- Short-term, fixed-amount loans: Simple interest often lowers total interest compared with compounding at the same nominal rate. For short terms (months), differences are small but measurable.
- Revolving debt (credit cards): Daily compounding and average daily balance calculations can magnify cost when balances carry month to month; paying early in the billing cycle reduces the average daily balance and interest.
- Savings, CDs, and investment accounts: Frequent compounding (monthly or daily) increases returns. For long horizons, compounding frequency and reinvestment drive dramatically different outcomes.
- Business loans: Many commercial loans compound interest or have interest accrual provisions that capitalize unpaid interest — read loan covenants carefully.
Real-world examples and worked comparisons
- Two lenders offer 6% nominal APR:
- Lender A: 6% compounded annually → EAR = 6.00%.
- Lender B: 6% compounded monthly → EAR = (1 + 0.06/12)^{12} − 1 ≈ 6.17%.
On a $100,000 balance, after 1 year Lender B costs about $170 more in interest than Lender A.
- Credit card scenario: $3,000 balance; card has 20% APR and uses average daily balance with daily periodic rate = 20%/365 ≈ 0.0548% per day. The longer you carry that balance within the billing cycle, the higher the average daily balance and the more interest you pay.
Common mistakes and how to avoid them
- Mistake: Comparing nominal APRs without adjusting for compounding frequency. Fix: Convert to EAR/APY.
- Mistake: Overlooking required fees (origination, maintenance, prepayment). Fix: Add fees to the principal or amortize them into the effective rate for apples-to-apples comparisons.
- Mistake: Assuming “daily” always means worse. Fix: Context matters — for savings accounts, daily compounding helps you; for loans, it increases cost.
Practical tips and strategies
- For borrowers: Ask lenders to show the effective annual rate (or compute it yourself). If you have variable-rate debt, understand how rates reset and whether accrual changes with a rate change.
- For savers: Favor accounts that compound daily or monthly, and confirm whether interest is credited and available for withdrawal immediately (look for “APY” on disclosures).
- For credit cards: Pay early in the billing cycle and pay more than the minimum to minimize interest because interest is charged on the average daily balance.
- Negotiate fees: Sometimes a slightly higher nominal rate with lower fees offers a lower effective cost.
FAQs (brief)
- Can I change the accrual method after signing a loan? Usually no — the accrual method is part of the contract. Changes require lender agreement and possibly an amendment.
- Does more frequent compounding always cost me more? For loans, yes (holding nominal rate constant). For investments, more frequent compounding increases returns.
- How do fees affect APR vs APY? APR typically shows interest cost without fees; APY includes compounding. To compare offers with fees, calculate an effective rate that spreads fees over the period.
Tools and resources
- Consumer Financial Protection Bureau (CFPB) — guidance on credit card interest and disclosure practices (consumerfinance.gov).
- IRS — general guidance on interest in tax contexts (irs.gov) and rates for underpayments/overpayments.
- Use our internal guides for deeper reading:
- Types of Interest Calculations: Simple, Compound, and Add-On (FinHelp) — https://finhelp.io/glossary/types-of-interest-calculations-simple-compound-and-add-on/
- Interest 101: How Compound Interest Works for Savers (FinHelp) — https://finhelp.io/glossary/interest-101-how-compound-interest-works-for-savers/
- Understanding Effective APR: Fees, Compounding, and Comparisons (FinHelp) — https://finhelp.io/glossary/understanding-effective-apr-fees-compounding-and-comparisons/
Professional disclaimer
This article is educational and based on general principles and experience. It does not constitute personalized financial, legal, or tax advice. Consult a qualified financial advisor, loan officer, or tax professional to assess how interest accrual methods apply to your specific situation.
Author note
In my practice, converting every offer to an effective annual rate and modeling at least two fee scenarios (best and worst case) prevents surprises. A small difference in compounding frequency can become large over a long loan or investment horizon—so do the math before you commit.
