What is loan amortization?
Loan amortization is the process of paying off a debt through regular installments over time. Each payment covers two components: interest — the cost of borrowing — and principal — the portion that reduces your outstanding balance. The proportion of each component changes every period depending on the amortization system chosen.
An amortization schedule is the complete period-by-period table that shows exactly how much of each payment goes to principal and how much to interest, along with the remaining balance after each installment. Lenders provide this table at loan origination; borrowers use it to plan prepayments, refinancing decisions, and total cost comparisons between competing loan offers.
The four main amortization systems
SAC (Constant Amortization System) repays the same principal amount every period. Because the outstanding balance decreases at a constant pace, the interest portion also shrinks each month — producing installments that start high and decrease steadily. SAC minimizes total interest paid over the life of the loan and is common in Brazil and other Latin American markets for mortgage and commercial loans.
Price (French System) produces fixed installments throughout the loan term. Early payments are heavily weighted toward interest; late payments are mostly principal. The constant payment simplifies cash flow planning — the borrower pays exactly the same amount every month. Because principal is repaid more slowly than in SAC, total interest is higher. Price is the most common system globally for personal loans, auto loans, and consumer credit.
Gradient (Progressive System) increases each installment by a fixed percentage every period. This structure is designed for borrowers whose income is expected to grow — for example, a business taking a loan against projected revenue growth. Initial installments are lower and more affordable; later installments compensate. The gradient rate controls how fast payments escalate.
Bullet (American System) requires interest-only payments throughout the loan term. The entire principal is repaid in a single lump sum at final maturity. Because the balance never decreases, interest accrues on the full principal for the entire term — making total interest cost the highest of all systems. Bullet loans are used in bridge financing, commercial real estate, and corporate bond structures where the borrower expects a liquidity event (asset sale, refinancing, or IPO) to fund the principal repayment.
SAC vs. Price: a worked example
Consider a loan of $100,000 at 1.5% per month for 24 months, starting January 2026, with no grace period.
Under SAC: monthly amortization = $100,000 ÷ 24 = $4,166.67. Month 1 interest = $100,000 × 1.5% = $1,500. First installment = $5,666.67. Month 24 interest = $4,166.67 × 1.5% = $62.50. Last installment = $4,229.17. Total interest paid ≈ $19,125.
Under Price: the constant installment M = P × [r(1+r)^n] / [(1+r)^n − 1] = $100,000 × [0.015 × (1.015)^24] / [(1.015)^24 − 1] ≈ $4,971.49/month. Month 1 interest = $1,500; principal = $3,471.49. Month 24 interest ≈ $73.47; principal ≈ $4,898.02. Total interest paid ≈$19,315 — about 1% more than SAC for this example. The gap widens with longer terms and higher rates.
The key tradeoff: SAC offers lower total cost but requires higher initial payments. Price offers payment stability at a slightly higher total cost. For most consumer borrowers, Price is easier to budget; for businesses focused on minimizing interest expense, SAC is preferable.
Grace periods: partial vs. total capitalization
A grace period defers the start of principal repayment. Under a partial grace period, the borrower pays only the interest accrued each month during the grace phase — the principal remains unchanged. Once the grace period ends, the full amortization schedule begins on the original principal.
Under a total (capitalized) grace period, no payment is made at all during the grace months. Accrued interest is added to the principal balance each period — a process called capitalization. This increases the base amount on which future interest is calculated, making it significantly more expensive than a partial grace period. A 3-month total grace on a $100,000 loan at 1.5%/month adds approximately $4,568 to the principal before amortization even begins.
Grace periods are common in project finance, infrastructure loans, and construction financing — contexts where the borrower needs time to generate revenue before servicing the debt. For consumer loans, they typically signal a weaker credit position and should be treated with caution due to their compounding cost.
How to convert between annual and monthly interest rates
Loan rates are quoted in different conventions depending on the market. Brazilian and Portuguese lenders often quote monthly rates directly; US and European lenders typically quote annual rates (APR or EAR). Converting between them correctly matters — the wrong formula can materially distort total cost comparisons.
Annual to monthly (compound): monthly rate = (1 + annual rate)^(1/12) − 1. Example: 19.56% annual → (1.1956)^(1/12) − 1 = 1.50%/month.
Monthly to annual (compound): annual rate = (1 + monthly rate)^12 − 1. Example: 1.5%/month → (1.015)^12 − 1 = 19.56%/year.
Avoid simple division (annual ÷ 12) for compound-interest products — it understates the effective monthly cost. This calculator accepts both monthly and annual inputs and performs the correct compound conversion automatically.
When to use each amortization system
Choose SAC when minimizing total interest is the priority and the borrower can handle higher early payments. Ideal for mortgage loans, corporate debt with strong initial cash flow, and any situation where the borrower wants to reduce exposure to interest rate risk quickly.
Choose Price when predictable monthly payments matter more than total cost. Best for personal loans, vehicle financing, and consumer credit where budget certainty is valued over interest savings.
Choose Gradient when cash flows are expected to grow over time — revenue-generating projects, startup financing, or investments with a ramp-up period. The initial lower payments align with the initial lower income phase.
Choose Bullet for short-term bridge financing or situations where a specific future event (asset sale, bond maturity, IPO) will fund the principal repayment. Never use for consumer lending — the interest-only structure can create a false sense of affordability while building significant end-of-term exposure.
Disclaimer: Results produced by this calculator are for informational and illustrative purposes only. They do not constitute financial, investment, legal, or tax advice. Actual loan terms, rates, and costs will vary depending on the lender, jurisdiction, borrower profile, and market conditions. Always review the official loan contract and consult a qualified financial professional before making borrowing decisions. Last updated June 2026. Sources: Banco Central do Brasil — Manual de Normas — Resolução CMN 4.935/2021; Consumer Financial Protection Bureau — What is an amortization schedule?(CFPB, 2024); Brealey, Myers & Allen —Principles of Corporate Finance, 14th ed.
