Loan Payment Calculator
Calculate monthly loan payments and total interest
Fast, accurate calculations with clear results. Built for speed and ease of use.
Formula
M = P[r(1+r)^n]/[(1+r)^n-1]M = monthly payment, P = principal, r = monthly rate, n = number of payments
How to Use Loan Payment Calculator
- Provide your input values.
- Understand the calculation method shown.
- Get immediate and accurate results.
- Use the output for planning or analysis.
Examples
This is the calculation behind every fixed-rate instalment loan, personal loans, car loans, and student loans, that pays off a fixed balance over a set number of equal payments. Each payment covers that period's interest first, with the remainder reducing the principal, so the interest portion shrinks and the principal portion grows with every payment even though the payment itself never changes.
The formula
M = P x [r(1+r)^n] / [(1+r)^n - 1]- M
- the fixed monthly payment
- P
- the amount borrowed
- r
- the monthly interest rate (annual rate / 12)
- n
- the total number of monthly payments
Worked example
A $20,000 car loan at 7% APR over 5 years has a monthly rate of 0.07 / 12 = 0.0058333 and n = 60 payments. Plugging in gives (1.0058333)^60 = 1.417626, so M = 20000 x 0.0058333 x 1.417626 / 0.417626 = $396.02 a month. Over the full 60 payments you repay $23,761.20 in total, of which $3,761.20 is interest.
What trips people up
- The rate has to be monthly, not annual. Dividing the annual rate by 12 before it enters the formula is the single most common mistake.
- n counts payments, not years. A 5 year loan paid monthly is n = 60, not n = 5.
- Extra payments do not simply subtract from the total, they reduce principal early and cut the interest charged on every payment after that.
- This formula assumes a fixed rate for the full term. A variable rate loan recalculates M whenever r changes.
Frequently asked questions
- Why does the interest portion of my payment shrink over time?
- Each payment's interest is charged on the remaining balance, which falls every month, so less of a fixed payment is needed to cover interest and more is left over to reduce principal.
- What happens to M if the interest rate is 0%?
- The formula divides by zero at r = 0 and breaks down; at a true 0% rate the payment is simply P / n, the principal spread evenly with no interest at all.
- Does a longer term always mean a smaller payment?
- Almost always, but the total interest paid over the life of the loan goes up, since more payments each carry their own interest charge even though every individual payment is smaller.
- How much does an extra payment toward principal actually save?
- It depends on how early in the term it lands. An extra payment in year one avoids far more future interest than the same extra payment in the final year, because more principal is still outstanding early on.
- Is this the same formula a bank uses to build my amortisation schedule?
- Yes, the fixed payment M comes from this formula, and the schedule is built by applying r to the remaining balance each period to split M between interest and principal.