Loan & EMI Calculator

The formula behind the payment

An amortising loan repays in equal instalments, each split between interest on the outstanding balance and principal that reduces it. The payment is fixed; the split within it changes every month.

The formula is P times r times one plus r to the power n, all divided by one plus r to the power n minus one, where P is the principal, r is the monthly interest rate and n is the number of payments.

The monthly rate is the annual rate divided by twelve. That is a convention rather than a compounding calculation, which is why a 12% annual rate becomes 1% monthly rather than the 0.949% that true monthly compounding to 12% annually would give.

Why early payments barely touch the balance

Interest is charged on the outstanding balance, which is highest at the start. So the first payment is mostly interest and very little principal.

On a £20,000 loan over five years at 8%, the first payment of £406 is £133 interest and £273 principal. The final payment is £3 interest and £403 principal.

Over a longer term the effect is dramatic. On a 25 year mortgage, roughly a third of the principal is still outstanding at the halfway point, which is why the amortisation schedule is worth looking at rather than just the monthly figure.

APR against the interest rate

The interest rate is what accrues on the balance. The annual percentage rate includes the interest plus compulsory fees, expressed as an annualised cost, and it is the figure designed for comparison.

Two loans at the same interest rate with different arrangement fees have different APRs, and the loan with the lower rate is not necessarily cheaper.

The representative APR advertised is the rate offered to at least 51% of successful applicants, which means nearly half may be offered worse. The rate you are actually quoted after an application is the only one that describes your loan.

Overpaying, and what it saves

An overpayment reduces the principal immediately, so all subsequent interest is calculated on a smaller balance. The saving compounds across the remaining term.

On a £200,000 mortgage over 25 years at 5%, overpaying £150 a month saves roughly £40,000 of interest and clears the loan around five years early.

The constraints are early repayment charges, which many fixed-rate products carry, and annual overpayment limits, commonly 10% of the balance. Both are in the agreement and both are worth checking before setting up a standing order.

What the calculation assumes

A fixed rate for the whole term. Variable and tracker rates change, and a payment calculated at today's rate describes today only.

No missed payments, no fees during the term, and no changes to the agreement. Late payment charges, arrears interest and any product transfer all alter the outcome.

It also assumes payments are monthly and equal. Some agreements have a different first payment, or a balloon payment at the end, or interest-only periods, and none of those follow the standard schedule. The agreement itself is the authority, and any material difference from a calculator's result is worth querying with the lender rather than assuming the calculator is right.

One further practical note about how lenders present numbers. The monthly payment is the figure that gets advertised because it is the one people compare, and it is the easiest to make look attractive by extending the term. Two loans with the same monthly payment can differ by thousands in total interest, and the total cost of credit is the figure that settles it. That number has to be disclosed in most jurisdictions, and it is worth finding on the paperwork rather than reading only the payment.