Loan amortization and repayment methods

Each payment contains principal and interest

Principal is the debt still outstanding; interest is the cost of using that balance. Compute monthly interest from the opening balance, subtract it from the payment, and the remainder repays principal. The closing balance becomes next month's interest base.

This model uses a fixed nominal annual rate i and monthly rate i/12. Term n counts months, not years. A 6% nominal annual rate means 0.5% monthly, not 6% monthly. Converting an effective annual rate is a different calculation from dividing by twelve.

Level payments: stable amounts, changing composition

Take a teaching loan of 1,200 at 6% nominal annually for 12 months. The first level payment is 103.28: interest is 1,200 × 0.5% = 6, principal repayment is 97.28 and the balance becomes 1,102.72. The second interest charge rounds to 5.51 on this smaller balance, allowing more of the payment to repay principal.

Early interest is higher because more debt remains outstanding, not because all future interest has been collected upfront. This cent-rounded ledger adjusts the final payment to 103.24 and totals 39.32 interest. The full schedule should show declining principal and a zero final balance.

Equal principal: larger early payments, declining interest

With the same principal, rate and 12-month term, equal-principal repayment returns 1,200/12 = 100 principal each month. Payments are 100 + 6 = 106 initially, 100 + 5.50 = 105.50 next, and 100 + 0.50 = 100.50 finally. Principal repayment stays constant while interest declines.

Total interest is 39.00 versus 39.32 for level payments, but the first payment requires 106 rather than 103.28. Compare early cash-flow affordability as well as total interest. The difference changes with term and rate; these amounts are not a universal mortgage saving.

Why zero rates and cent rounding need special treatment

At zero interest, 1,200 over 12 months is 100 per month. Use the P/n branch instead of inserting zero into an annuity expression that would become 0/0. Principal repayments must still sum to the loan and the final balance must be zero.

The calculator rounds monthly interest and payments to cents, then settles the remaining principal in the final payment. Its ledger can differ by a few cents from a textbook calculation retaining unlimited precision at every step. Rounding is an accounting convention, not permission to change principal or ignore a residual payment.

Use the interaction to compare funding pressure

Hold principal, rate and term fixed when switching repayment methods. Compare payments, interest and the balance path. A higher rate increases the cost of outstanding debt. A longer term may reduce monthly payments but leaves debt outstanding longer and can increase total interest; those outcomes are compatible.

The model assumes month-end payments and a fixed rate, with no grace period, fees or prepayment. It supports up to 1,200 months and annual rates from 0–100%. Contracts may accrue interest daily or use variable rates and additional charges. Use this schedule to understand trade-offs, not as a bank quote.

Scope and limitations

Fixed nominal annual rate/12, month-end payments, no grace period, fees or prepayment. Monthly interest/payments round to cents, with a final balance adjustment; bank daily-accrual contracts may differ. Up to 1,200 months; annual rate 0–100%.