Loan / EMI calculator

What the payment is made of

A repayment loan is priced so that the same amount leaves your account every month and the debt is gone by the end. Each instalment covers the interest that has built up on whatever is still owed, and the remainder comes off the balance. Because the balance shrinks, the interest portion shrinks with it and the principal portion grows, the payment stays still while its two halves trade places.

That is why the year-by-year table matters more than the monthly figure. Early on, most of the money is rent on the debt rather than repayment of it. On a long loan the crossover, the point where more than half of each payment starts clearing the balance , can be a third of the way in.

The formula

Payment = P x r / (1 - (1 + r)^-n), where P is the amount borrowed, r is the monthly interest rate and n is the number of months. The monthly rate is the annual rate divided by twelve, which is what lenders mean when they quote a monthly rate and what published EMI figures use.

At a rate of zero that formula divides by zero, so this calculator handles it separately: the payment becomes the amount divided by the number of months, which is what an interest-free loan actually costs.

What this does not include

The figure is the cost of the loan and nothing else. Arrangement, broker and valuation fees, mortgage or payment protection insurance, property tax collected alongside a mortgage, and early repayment charges are all excluded, because each depends on the lender and the country rather than on the loan. A real bill is usually larger.

The rate is also assumed to hold for the whole term. A tracker will move, and a fixed rate that ends after two or five years will be replaced by whatever is available then. If you are on a fix, it is worth running the calculation twice, once on the fixed rate and once on a pessimistic one, to see what the payment could become.

Term against total

Lengthening the term is the easiest way to make a monthly payment affordable and the most expensive. Stretching a loan from five years to seven lowers each payment but adds two more years of interest charges, and the total can rise by a third or more. Compare offers on the total paid and on the interest as a share of what you borrowed; both are shown above the table.

Overpaying works in the opposite direction, and disproportionately so: money paid early removes interest for every remaining month of the term. This calculator assumes you pay exactly the scheduled instalment, so its total is the figure to beat rather than the one to expect.