Loan and Mortgage Formula Reference
A stronger printable reference for loan and mortgage repayment, amortisation logic, interest allocation, and payment comparisons across different terms.
Formula highlights
What this pack covers
This guide keeps the standard repayment formula, amortisation logic, and practical term trade-offs visible when comparing borrowing options.
Core relationships
- payment = P x i / (1 - (1 + i)^(-n))
- interest each period = balance x periodic rate
- principal repaid = payment - interest
- total interest = total payments - original principal
How to read the payment
The payment is not a flat principal slice. It starts interest-heavy and becomes principal-heavy over time as the balance falls.
Worked example: term comparison
Longer terms usually lower the monthly payment while increasing total interest. Shorter terms do the reverse. The right choice therefore depends on affordability and lifetime cost together.
Extra-payment reminder
Extra principal paid early usually has an outsized effect because it reduces the balance on which future interest is calculated.
Common limits
- Pure formulas do not automatically include fees, insurance, taxes, or future rate changes.
- A payment that fits today may still need stress-testing against changing conditions.
Use the formulas in live tools.
Loan Payment Calculator
Calculate a fixed-payment loan from the amount borrowed, rate, and term, using only the values you enter.
Mortgage Payment Calculator
Estimate a standard repayment mortgage from property price, deposit, rate, and term with clear monthly costs and supporting figures.