Types of Interest Calculations: Simple, Compound, and Add-On

Understanding how interest is calculated is one of the fastest ways to improve financial decisions. The math can be straightforward, but the terms lenders use—and the way interest is applied—can dramatically change what you actually pay or earn. Below I explain each type, show formulas and examples, compare effective rates, and give a short checklist you can use before taking a loan or choosing an account. (In my 15 years advising clients, borrowers most often underestimate the impact of compounding frequency and add-on pricing.)

Quick historical note

Interest and lending practices have existed for millennia (ancient Mesopotamia used early loan contracts). Modern finance formalized simple and compound interest formulas; add-on interest is a later practical construct used in some consumer loan products. Today regulators require APR disclosure for most consumer loans so borrowers can compare offers more fairly (CFPB guidance on APR disclosure explains required disclosures: https://www.consumerfinance.gov).

How each interest type works (formulas and plain-English examples)

1) Simple interest

• Formula: SI = P × r × t
• P = principal (starting balance)
• r = annual interest rate (decimal)
• t = time in years

Example: Borrow $1,000 at 5% simple interest for 3 years.

• Interest = 1000 × 0.05 × 3 = $150
• Total repayment = 1000 + 150 = $1,150

When simple interest is used on an amortizing loan, interest for each period is computed on the remaining principal only. Simple interest is common for short-term loans and some auto or personal loans.

2) Compound interest

Compound interest applies interest to the principal and to interest that has already been added (interest-on-interest). The faster the compounding periods (monthly vs annually), the higher the effective yield or cost.

• Formula: A = P × (1 + r/n)^(n×t)
• A = future value after t years
• n = number of compounding periods per year

Example: $1,000 at 5% compounded annually for 3 years.

• A = 1000 × (1 + 0.05/1)^(1×3) = 1000 × (1.05)^3 = $1,157.63

If compounding is monthly instead of annually, APY (annual percentage yield) increases slightly:

• APY = (1 + r/n)^n − 1
• For r = 5% with monthly compounding (n = 12): APY ≈ (1 + 0.05/12)^12 − 1 ≈ 5.116%

Compound interest is how savings accounts, CDs, and investment accounts grow most efficiently. See our deeper examples on compound interest for visuals and step-by-step growth tables: “Understanding Compound Interest with Simple Examples” (https://finhelp.io/glossary/understanding-compound-interest-with-simple-examples/).

3) Add-on interest

Add-on interest computes total interest using the original principal for the whole term, then adds that interest to the principal to form the repayment amount. Payments are often equal installments based on that inflated balance.

• Total add-on interest = P × r × t
• Repayment total = P + total add-on interest

Example: $1,000 at 5% add-on for 3 years.

• Total interest = 1000 × 0.05 × 3 = $150
• Total repayment = $1,150
• If repaid monthly over 36 months: monthly payment = 1150 / 36 ≈ $31.94

Why this can be costly: because interest is calculated on the full original principal even as your outstanding principal declines with each payment, the effective interest rate is higher than the quoted rate. A quick approximation for effective annual rate with equal payments is:

• Effective rate ≈ (total interest / average outstanding balance) / years
• Average outstanding balance for equal installments ≈ P/2
• Using the $1,000 example: effective rate ≈ (150 / (1000/2)) / 3 = (150 / 500) / 3 = 0.10 = 10% per year (approx)

Note: That approximation illustrates why an add-on 5% loan can act like a 10% loan when amortized.

Comparing APR, interest rate, and APY

• Interest rate (nominal) typically refers to the stated annual rate on the loan or investment.
• APR (annual percentage rate) reflects the annual cost of borrowing including some fees and the effects of interest calculation; it’s the standard comparison tool for loans (see CFPB guidance: https://www.consumerfinance.gov/consumer-tools/credit-cards/credit-card-terms/annual-percentage-rate/).
• APY (annual percentage yield) tells savers the annual return including compounding.

For loans with add-on interest, the APR disclosed should account for the payment schedule and fees. When comparing offers, compare APRs and read the loan terms for how interest is applied. Our article “Understanding Effective APR: Fees, Compounding, and Comparisons” explains how fees and compounding change the effective cost (https://finhelp.io/glossary/understanding-effective-apr-fees-compounding-and-comparisons/).

Real-world scenarios and practical calculations

1) Add-on vs simple example (practical): A borrower chooses between two $5,000, 3-year loans:

• Loan A: Simple interest 6% (interest calculated on outstanding principal monthly, amortized)

• Loan B: Add-on interest 6% (calculated on full $5,000 for 3 years)

  For Loan B: Total add-on interest = 5000 × 0.06 × 3 = $900, repayment = $5,900, monthly payment = 5900 / 36 ≈ $163.89. Using the average balance approximation, Loan B’s effective annual rate will be meaningfully higher than 6%.

  Loan A’s monthly interest declines as principal is repaid, so its effective cost will be lower. Always ask for an amortization schedule and the APR.

2) Savings example showing APY benefit: A 5% nominal rate compounded monthly has APY ≈ 5.116%. Over long periods that difference compounds—small APY gains matter for large balances.

How to compare loan offers — a short checklist

• Ask whether interest is simple, compound, or add-on and get the exact formula or amortization schedule.
• Request the APR and an amortization table showing monthly payments and interest vs principal portions.
• Check for fees (origination, prepayment penalties) and make sure they’re included in APR comparisons.
• Convert quoted add-on or unusual methods into an effective APR (ask lender or use an online loan calculator).
• For savings, compare APY rather than the nominal rate and verify compounding frequency (daily, monthly, annually).

Common mistakes to avoid

• Treating the quoted rate as the true cost without checking APR or compounding.
• Assuming add-on loans are identical to simple-interest loans.
• Ignoring fees when comparing loan offers; fees can push APR much higher.

Practical tips I use with clients

• Always get an amortization schedule before you sign. It shows exactly how much interest you’ll pay each period.
• If a loan quote lacks an APR or amortization, insist on it or walk away. Reputable lenders provide clear APR disclosures (CFPB rules require consumer disclosures).
• For short-term borrowing, simple-interest loans can be cheaper; for long-term savings, compound interest with frequent compounding helps the most.

Resources and further reading

• Consumer Financial Protection Bureau — APR and loan disclosures: https://www.consumerfinance.gov
• For hands-on examples of compound growth, see “Understanding Compound Interest with Simple Examples” (https://finhelp.io/glossary/understanding-compound-interest-with-simple-examples/).
• To learn more about how fees, compounding, and APR compare, read “Understanding Effective APR: Fees, Compounding, and Comparisons” (https://finhelp.io/glossary/understanding-effective-apr-fees-compounding-and-comparisons/).

Professional disclaimer

This article is educational and not individualized financial advice. In my practice I help clients run these comparisons on real offers before they commit. For decisions that affect your taxes, retirement, or business financing, consult a licensed financial professional and review official disclosures from lenders and regulators (CFPB, IRS). The U.S. Internal Revenue Service publishes guidance on interest and tax treatment of certain interest items (https://www.irs.gov).

Sources

• Consumer Financial Protection Bureau (CFPB) — consumer guides to APR and loan disclosures: https://www.consumerfinance.gov
• U.S. Internal Revenue Service — general guidance on interest and taxation: https://www.irs.gov

If you want, I can run a side-by-side effective APR comparison for two real loan spreadsheets you provide (principal, stated rate, term, fees, compounding).”