Loan Tenure (Loan Tenure) Calculator
From principal, annual rate and monthly payment, back-solve the months/years to clear and the total interest.
Input Data
Results
At a glance:Under amortising repayment, given principal P, monthly rate r and monthly payment M, the periods n are solved from the annuity formula: n = −ln(1 − P×r ÷ M) ÷ ln(1+r). If M ≤ P×r (only covers interest) it never clears — the tool reports no solution. Total interest = M×n − P.
Formula
Monthly rate r = annual ÷ 12.
n = −ln(1 − P×r ÷ M) ÷ ln(1+r) (when M > P×r).
Total interest = M × n − P.
How to Use
- Enter the loan principal and annual rate.
- Enter the monthly payment you can afford.
- View the periods, years and total interest to clear.
Case Studies
1,000,000 at 4%, monthly 5,500
r = 4% ÷ 12 = 0.003333.
P×r = 3,333 < 5,500 (can clear).
n ≈ −ln(1 − 3,333/5,500) ÷ ln(1.003333) ≈ 245 months (~20.4 years); total interest ≈ 348,500.
FAQ
Why can a too-low payment never clear?
If the monthly payment ≤ that month's interest (P×r), the principal never drops — you only pay interest. When M ≤ P×r the tool reports no solution; raise the payment.
How does this differ from the EMI calculator?
The EMI calculator gives the term and computes the payment; this reverses it — give the payment, get the term. They complement each other: set a budget, then check if the term is feasible.
Why may the periods be a decimal?
The formula is a continuous solution; the actual last period is slightly adjusted (tail rounding). The integer months shown is approximate and total interest is estimated — use the lender's statement for the final period.
Should I use the APR?
Preferably the Annual Percentage Rate (APR), which includes fees spread out. Using the nominal rate alone understates the interest. HK mortgages are mostly Prime or H-Plan linked.
Does early repayment shorten the term?
Yes. This tool assumes a fixed payment without extra principal; occasional early repayment shortens the actual term and interest. Treat early repayment as raising the monthly to re-estimate.
What limits the max term of a HK mortgage?
HK mortgages are usually capped at 30 years, plus an 'age + term' limit (e.g. 75 or 80) and a stress test. This tool does not cap the term — it is only a mathematical back-solve.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.