Monthly payment = principal × r × (1+r)ⁿ ÷ [(1+r)ⁿ − 1]. $1M at 3.0% for 30 years → $4,216/mo, $518k total interest. Covers both repayment methods, rate tables, prepayment strategy and 6 proven ways to cut interest.
Key Takeaways
Annuity formula: payment = P × r × (1+r)ⁿ ÷ [(1+r)ⁿ − 1], where r = monthly rate, n = months
$1M / 30yr / 3.0%: annuity $4,216/mo with $518k interest; equal principal saves $67k
Rate sensitivity: each 0.1pp rate change moves the payment ~$50/mo per $1M over 30 years
Top savings levers: shorter term, biweekly payments, early prepayments, HPF conversion, refinancing
Core answer: equal-payment monthly payment = loan × monthly rate × (1+r)ⁿ ÷ [(1+r)ⁿ − 1]. ¥1M, 30 years, 3.0%: payment ¥4,216/month, total interest ¥518k. Every 0.1pp lower rate saves ~¥20k over 30 years — negotiating the rate beats haggling the house price.
The payment formula
Equal payment (fixed monthly):
Payment = P × r × (1+r)ⁿ ÷ [(1+r)ⁿ − 1]
P = principal, r = monthly rate (annual ÷ 12), n = total periods (years × 12)
Equal principal (declining):
Month k payment = P ÷ n + (P − principal repaid) × r
Hand-math errs easily — use the calculator: loan amount, term, rate, done.
Latest mortgage rates (2025)
Loan type
Rate
Notes
Commercial (first home)
~3.0%-3.3%
5Y LPR 3.5% minus 20-50bp
Commercial (second home)
~3.3%-3.9%
Local markups vary
Housing fund (first, 5Y+)
2.6%
After the May 2025 cut
Housing fund (second, 5Y+)
3.075%
≥ 1.1× first-home rate
Two repayment methods compared
¥1M / 30Y / 3.0%:
Item
Equal payment
Equal principal
Monthly
¥4,216 fixed
¥5,278 first month, −6.9/month
Total interest
¥518k
¥451k
Best for
Stable income, cash-flow safety
High income, interest savings
See the dedicated Equal Payment vs Equal Principal guide for the full breakdown.
Affordability red lines
Bank approval line: payment ≤ 50% of monthly income (income proof must cover 2× payment)
Financial safety line: payment ≤ 40% of household take-home income
Emergency reserve: at least 12 months of payments in cash/money funds
Five money-saving tactics
Max out the housing fund first: 2.6% vs 3.0%+ saves ~¥80k per ¥1M over 30 years; combine with commercial loan if the fund quota falls short
Negotiate the rate markup: banks in the same city differ by 20-50bp — ask at least three
Term shortening beats payment reduction: when prepaying, choose "same payment, shorter term" — roughly 1.5× the interest saving of the alternative
Prepay in the golden window: for equal payment, the first third of the term is when prepayment saves most — the interest bulk is already paid after that
Pick the LPR repricing date wisely: in a falling-rate cycle, Jan 1 repricing passes cuts through faster
Common mistakes
"A 30-year loan means working for the bank": inflation dilutes long-term debt. A ¥1,000 payment was a fortune in 1995 and pocket change by 2015. Long-term low-rate mortgages are the best leverage ordinary people ever get.
"Prepay as early as possible, always": compare the opportunity cost. If your investments reliably beat the mortgage rate, prepaying loses money; if not, prepay early.
"More interest with equal payment = being ripped off": both methods charge interest on the remaining balance. Equal payment totals more interest purely because the balance falls slower — the bank collects nothing extra.
Frequently Asked Questions
How is the monthly mortgage payment calculated?
Payment = P × r × (1+r)ⁿ ÷ [(1+r)ⁿ − 1]. For $1M at 3.0% (r = 0.0025) over 360 months: 1,000,000 × 0.0025 × (1.0025)³⁶⁰ ÷ [(1.0025)³⁶⁰ − 1] = $4,216. The formula amortizes the loan so each payment covers that month's interest plus a growing slice of principal.
How much interest do I save with a shorter term?
$1M at 3.0%: 30 years costs $518k interest; 25 years $423k (save $95k); 20 years $331k (save $187k); 15 years $243k (save $275k). The 20-year payment is $5,546 — 31% higher monthly for 36% less interest. Match the term to your comfortable payment-to-income ratio, not the maximum the bank offers.
Should I choose equal payment or equal principal?
Equal principal saves interest ($67k on $1M/30yr/3.0%) but starts $1,062/mo higher and only drops below the annuity payment in year 11. Choose it if the first-month payment stays under 40% of income or you plan early payoff. Otherwise annuity plus occasional prepayments gives flexibility with similar lifetime cost.
Is prepaying my mortgage worth it?
Yes when your mortgage rate exceeds your safe investment return. At 3.0%+, a guaranteed 3% "return" by prepaying beats most deposits. Best timing: the first 5-8 years when payments are interest-heavy. Keep 6 months of expenses in cash first, and check for prepayment penalties (usually waived after 1-3 years).
Shorten the term or reduce the payment when prepaying?
Shortening the term saves roughly 2-3× more interest than reducing the payment on the same prepayment. $200k prepaid on a $1M/30yr/3.0% loan in year 3: term-shortening saves ~$180k interest; payment-reduction saves ~$75k. Choose payment-reduction only if monthly cash flow is tight.
How does a rate change affect my payment?
Most mortgages reprice annually on the reset date. Per $1M over 30 years, every 0.1pp moves the annuity payment ~$50/mo and total interest ~$20k. A 0.5pp cut on $1M saves ~$250/mo. Track your reset date and the reference rate — refinancing or HPF conversion may beat waiting.