How EMI Is Calculated

The formula

EMI = P × r × (1+r)^n / ((1+r)^n − 1)

P is the principal — the amount you actually borrow. r is the monthly interest rate, found by taking the annual rate your lender quotes, dividing by 12 (months), then by 100 (to convert a percentage to a decimal). n is the number of monthly payments — the tenure in months, not years.

Why the formula looks the way it does

A loan doesn't charge interest once on the full amount — it charges interest on whatever balance remains at that point in the loan. If EMI were just (principal + total interest) ÷ number of months, early payments would be undercharged for interest and late payments overcharged, since the remaining balance shrinks over time. The formula above is derived so that a fixed monthly payment, applied to a shrinking balance at a constant periodic rate, exactly pays off the loan (principal and all accrued interest) at the final payment — no more, no less.

Worked example

Say you borrow Rs. 10,00,000 at 10% annual interest for 5 years (60 months).

r = 10 ÷ 12 ÷ 100 = 0.008333 n = 60

EMI = 10,00,000 × 0.008333 × (1.008333)^60 / ((1.008333)^60 − 1) ≈ Rs. 21,247

Over 60 months you pay 60 × 21,247 ≈ Rs. 12,74,820 total — meaning about Rs. 2,74,820 is interest. Notice this is more than a naive "10% of 10,00,000 for 5 years = Rs. 5,00,000" guess would suggest, precisely because interest compounds monthly on the remaining balance, not a flat calculation on the original principal.

Reducing balance vs. flat-rate loans

Almost all bank loans in Nepal (home, vehicle, personal) use reducing-balance interest, which is what the formula above computes. A small number of informal or flat-rate loans instead charge interest on the original principal for the whole tenure, regardless of how much you've repaid — which sounds similar but produces a noticeably higher effective interest cost for the same quoted rate. Always ask your lender explicitly whether a quoted rate is reducing-balance or flat before comparing offers.

Common mistakes when estimating EMI by hand

Using the annual rate directly instead of dividing by 12 first; forgetting that the formula's exponent applies to (1+r), not r alone; and comparing a flat-rate loan's headline percentage directly against a reducing-balance loan's percentage as if they meant the same thing. Our EMI Calculator does the compounding math for you and produces the full month-by-month breakdown, which is the easiest way to sanity-check any deal you're offered.