Estimate the monthly payment from a loan amount, or from a price minus a down payment, plus an annual rate and a term in years. The wording is for comparing a home loan. The math is a generic amortizing loan: no stress test and no loan-to-value cap.
The monthly payment (M) pays off a loan amount (P) over n months at a monthly interest rate r. The annual rate is divided by 12, and the term in years is multiplied by 12.
M = P × r × (1 + r)^n / ((1 + r)^n − 1)
A zero rate charges no interest. The payment is only the loan split across the months:
M = P / n
Total paid is the monthly payment multiplied by the number of months. Total interest is total paid minus the loan amount. That formula holds when the extra monthly payment is blank or zero. When the extra is greater than zero, total paid is the cash actually paid, and the loan can end before n months.
Each year of the summary adds up to twelve months of payments (fewer in a final partial year). Interest for a month is the balance at the start of that month times r. Principal is the payment minus that interest. The balance at the end of the term is zero.
Total paid = M × n. Total interest = total paid − P.
1,000,000 at 3% for 30 years is about 4,216.04 a month. At a zero rate the same loan is 1,000,000 divided by 360 months.
An extra monthly payment is applied to principal after the contractual split of the monthly payment into interest and principal. The contractual payment M does not change.
The last month pays only the remaining balance plus that month’s interest. Months saved and interest saved compare this result with the same loan and no extra.
Months saved = n − months paid. Interest saved = (M × n − P) − total interest.
The rate stays fixed for the whole term. Payments are monthly, interest compounds monthly, and the loan is fully amortizing. A monthly extra payment is included when entered. Fees, insurance, rate changes, a one-time prepayment, prepayment penalties, and offset accounts are not included.
This does not apply a Hong Kong stress test, a debt-servicing ratio, or a loan-to-value cap. Amounts stay in one currency. The figure is an estimate, not a bank offer and not financial, investment, or tax advice.
The page uses the standard amortizing formula. The annual rate is divided by 12, the term in years becomes a number of months, and the payment is the fixed amount that is scheduled to bring the balance to zero on the last month. If the rate is zero, the payment is the loan amount divided by the number of months.
Yes. Choose that option and the loan amount is the price minus the down payment. You can also type the loan amount directly. After that, the formula is the same.
Each year shows principal paid, interest paid, and the balance left at the end of that year. Across the full term, principal paid adds up to the loan amount and interest paid adds up to the total interest.
No. The page is written for someone comparing a home loan, including the usual idea of a monthly repayment over a term of years, but the math is generic. It does not apply a stress test, a debt-servicing ratio, or a loan-to-value cap.
Fees, mortgage insurance, a rate that changes, a one-time prepayment, prepayment penalties, and an offset account are not included. A monthly extra payment is included when you enter one. The rate you enter stays fixed for the whole term.
No. It is an estimate from the numbers you type. A lender can quote a different payment. This is not financial, investment, or tax advice.