A loan's monthly payment depends on three variables: the principal (amount borrowed), the interest rate, and the loan term. All standard bank loans use the amortisation formula below.
The amortisation formula
M = P × r × (1+r)^n / ((1+r)^n - 1)
Where:
- M = monthly payment
- P = principal (loan amount)
- r = monthly interest rate = annual rate ÷ 12
- n = total number of payments (months)
Example: £200,000 over 25 years at 4.5% APR
- r = 4.5% ÷ 12 = 0.375% = 0.00375
- n = 25 × 12 = 300
- M = £200,000 × 0.00375 × (1.00375)³⁰⁰ ÷ ((1.00375)³⁰⁰ − 1) ≈ £1,111/month
Impact of loan term on cost
| Term | Monthly payment (£200k at 4.5%) | Total interest paid |
|---|---|---|
| 10 years | £2,072 | £48,640 |
| 15 years | £1,529 | £75,220 |
| 20 years | £1,265 | £103,600 |
| 25 years | £1,111 | £133,300 |
| 30 years | £1,013 | £164,680 |
APR vs interest rate
The Annual Percentage Rate (APR) includes the nominal interest rate plus all mandatory fees (arrangement fees, compulsory insurance). Always compare APRs - not headline interest rates - when choosing between loan products.