How equal-instalment mortgages work: the formula, the split and early repayment.

The formula and the monthly rate

The equal-instalment formula is: payment = principal × monthly rate × (1 + monthly rate)^months ÷ [(1 + monthly rate)^months − 1], where the monthly rate is the annual rate ÷ 12 and months = years × 12. For 1,000,000 over 30 years at 3.1%, the monthly rate is about 0.2583% and the term is 360 months, giving a payment of roughly 4,270 yuan, total repayment of about 1.537 million and therefore about 537,000 in interest. Those three numbers are the basis for judging whether the loan suits you.

How each payment splits into principal and interest

Equal instalments keep the payment constant while the internal split shifts. First-month interest is the outstanding principal × monthly rate, about 2,583 yuan, leaving roughly 1,687 yuan of principal. As the balance falls, interest falls and principal rises; it takes about ten years for the principal portion to overtake interest, and in the final month interest is only a dozen yuan or so. That is the intuition behind early repayment: the sooner you pay, the more future interest you cancel, because you are removing principal that would otherwise keep accruing interest.

Equal instalment or equal principal

Same 1,000,000, 30 years, 3.1%: equal instalments give a constant 4,270 per month and about 537,000 interest; equal principal starts at about 5,361 and falls by roughly 7 yuan a month, with about 466,000 interest — roughly 70,000 less, but with visibly heavier early years. The practical rule: if the payment already exceeds 40% of household income, choose equal instalments to protect cash flow; if income is high and stable and you plan to repay early within a few years, equal principal saves more interest. The goal is not the theoretical optimum but a payment you can sleep with.

LPR and repricing

Most mortgages are now priced as LPR plus a fixed spread: the spread is locked for the contract term while the LPR floats with the market. Most contracts reprice once a year (commonly 1 January or the disbursement anniversary), so a fall in the LPR usually shows up in your payment only on the next repricing date. Always calculate with your current effective rate rather than the original contract rate, or the error will be large.

Early repayment: shorter term or smaller payment

The choice is between saving interest and reducing pressure. Shortening the term (payment roughly unchanged) saves more total interest and suits stable incomes and a wish to finish sooner; lowering the payment (term unchanged) eases the monthly burden immediately and suits tight cash flow or better investment options. Three cautions: some banks charge penalties or set minimum amounts, so check the contract and app first; with a combined fund-plus-commercial loan, clearing the commercial part usually pays off more; and if your mortgage rate is clearly below what you can earn safely, early repayment deserves a fresh calculation.

Why your figure differs from the bank’s

Four usual causes: the bank’s rounding rules (to the yuan or to the cent); a first period shorter than a month, charged by actual days; different repricing dates, so the effective rate changes within the year; and housing-fund and commercial portions accruing separately before being added together. Differences within a few dozen yuan are normal conventions rather than arithmetic errors. For cent-level precision use the bank’s repayment schedule; these tools are for estimating and comparing before you decide.

想马上动手：用 房贷计算器 把你的金额、年限与利率填进去，两种还款方式各算一遍再对比；也可以先看 生活与财务计算专题 的其他工具。Try it now: enter your amount, term and rate in the mortgage calculator and compare both repayment styles, or browse the rest of the everyday calculator collection.

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