Annuity or declining payments
Annuity payments are equal every month. At the start most of each payment goes to interest; by the end most of it repays the principal. This is the usual choice for mortgages and consumer loans because the payment is predictable.
With declining (differentiated) payments the principal is repaid in equal parts and the interest is charged on the remaining balance. The first payment is the largest, every next one is smaller, and the total interest is lower than with an annuity.
Formulas
The monthly rate is r = annual rate / 12 / 100, and n is the number of months.
- Annuity payment: P × r / (1 − (1 + r)−n), where P is the loan amount.
- Declining payment in month k: P / n + (remaining balance) × r.
Payments are rounded to cents, and the last payment is adjusted so the balance reaches exactly zero. Lenders often charge interest by the actual number of days in each month, add fees and insurance, so your bank's schedule may differ by a few units of currency.
Example
A loan of 300,000 at 12% a year for 3 years with annuity payments costs 9,964.29 a month; the total interest is 58,714.58. With declining payments the first payment is 11,333.33, the last is 8,416.78, and the total interest is 55,500.00.