Loan Amortization Calculator
Calculate the monthly instalment, total repayment and total interest of an equal-instalment (amortising) loan, with the first-period interest/principal split.
Input Data
Results
At a glance:Loan amortization is the process of repaying a loan by equal instalments: the instalment is fixed, but the interest-to-principal ratio shifts over time — high outstanding balance early means a larger interest share; the principal share grows later. Core formula: monthly rate r = annual rate% ÷ 100 ÷ 12, total periods n = years × 12; monthly payment = principal × r × (1+r)^n ÷ ((1+r)^n − 1); first-period interest = principal × r, first-period principal = monthly payment − first-period interest; total repayment = monthly payment × n, total interest = total repayment − principal. Example: principal HK$500,000, annual rate 5%, 20 years: monthly payment ≈ HK$3,299.78, first instalment interest ≈ HK$2,083.33 and principal ≈ HK$1,216.45; over 20 years total repayment ≈ HK$791,947, total interest ≈ HK$291,947. The first-period split shows why the balance falls slowly early and why early repayment saves the most interest. This is a simplified model assuming a fixed rate and on-time payments; actual repayment follows the lender's contract.
Formula
Monthly rate r = annual rate% ÷ 100 ÷ 12; total periods n = years × 12.
Monthly payment = principal × r × (1+r)^n ÷ ((1+r)^n − 1).
First-period interest = principal × r; first-period principal = monthly payment − first-period interest.
Total repayment = monthly payment × n; total interest = total repayment − principal.
$$M = P \times \dfrac{r\,(1+r)^n}{(1+r)^n - 1}$$$$\text{Interest}_1 = P \times r,\quad \text{Principal}_1 = M - \text{Interest}_1$$$$\text{Total} = M \times n,\quad \text{Interest} = \text{Total} - P$$How to Use
- Enter the loan principal.
- Enter the annual rate and repayment term.
- View the monthly payment, total repayment, total interest and the first-period interest/principal split.
FAQ
Why does the balance fall so slowly at the start?
With an equal-instalment (amortising) loan, each instalment is fixed and interest is charged on the outstanding balance. Early on the balance is highest, so most of the payment goes to interest and only a small part reduces the principal; as the balance drops, interest shrinks and the principal share gradually rises. This is exactly what the first-period split illustrates.
How much interest can early repayment save?
Because interest is charged on the outstanding balance, any extra repayment directly reduces the principal, so interest in every later period falls too — saving a substantial amount over time and shortening the term. This tool does not compute early repayment directly, but the first-period split shows that repaying principal early (when it carries interest the longest) yields the biggest saving.
What is the difference between this and a mortgage calculator?
Amortization is the generic equal-instalment repayment model and applies to all kinds of instalment loans; a mortgage calculator is built specifically for property loans and may additionally consider the down-payment ratio, mortgage insurance or stamp duty. The core instalment formula is the same — this tool focuses on showing the general principal-and-interest amortization structure.
Do Hong Kong mortgages mostly use equal-instalment amortization?
Yes. The vast majority of Hong Kong residential mortgages use equal-instalment amortization (fixed monthly payment with a shifting interest/principal mix), matching this calculator's model. However, Hong Kong mortgage rates are mostly floating (tied to HIBOR or the prime rate P), so when the rate changes the payment or term is adjusted. This tool assumes a fixed rate; to simulate a rate change, run separate scenarios at different rates.
Will the monthly payment here match what the bank actually charges?
It will be very close, but not necessarily exact. Differences can come from the bank's interest basis (actual days vs. equal monthly), rounding conventions, and various fees (legal, mortgage insurance, handling) not included here. If you have cash rebates or penalty periods, your real cost differs too. This calculator is good for understanding amortization and estimating the payment; the bank's repayment schedule remains the official figure.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.