Loan EMI Calculator
Equated Monthly Instalment, total interest, and amortisation for a loan
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What this calculator computes
The Loan EMI (Equated Monthly Instalment) calculator computes the fixed monthly payment that repays a loan over a stated term at a stated annual interest rate, plus the total interest paid over the loan's life. The formula is EMI = P × r × (1+r)^n / ((1+r)^n − 1), where P is the loan principal, r is the monthly interest rate (annual rate / 12), and n is the number of monthly payments. The EMI structure means each monthly payment is identical, but the split between interest and principal changes over the loan's life: in early payments most of the EMI goes to interest (because the outstanding balance is high), while in later payments most goes to principal (because the balance has shrunk). This is amortisation, and it is why a 25-year mortgage's first decade pays mostly interest and the last decade pays mostly principal. The calculator returns the EMI, the total payable (EMI × n), the total interest cost (total payable − principal), and the year-by-year balance projection so the amortisation curve is visible. EMI is the standard repayment structure for mortgages, car loans, personal loans, and most installment finance products in the UK, US, EU, and India (where the term "EMI" originates and is most commonly used). **Educational tool only — not financial advice. Real loan offers include arrangement fees, early-repayment charges, payment-protection insurance, and sometimes fixed-rate-period revert clauses that the calculator does not model. Compare APR figures, not headline interest rates, and consult a qualified mortgage adviser or financial advisor for any major borrowing decision.**
Calculator
The formula
Formula
EMI = P × r × (1+r)^n / ((1+r)^n − 1)
Worked example
When to use this calculator
Use this calculator before applying for any amortising loan — mortgage, car loan, personal loan, or business installment loan — to verify the lender's quoted monthly payment, project the total cost of borrowing over the loan term, and compare alternative term-and-rate combinations. The most useful comparisons are term-length sensitivity (how much extra do I pay monthly to clear in 20 years vs 25?) and rate-difference sensitivity (how much does a 0.5% rate cut save over the term?). For mortgages, the calculator provides the headline number but does not model fixed-rate revert clauses (where the rate changes after 2–5 years), arrangement fees, valuation fees, early-repayment charges, or any associated insurance products — the true cost of borrowing as quoted by APR includes these. Use the APR figure for the lender's actual cost-of-credit number, not the headline interest rate. The calculator also does not handle interest-only mortgages, where the principal is not amortised and only interest is paid each month.
Common input mistakes
- Using the annual rate directly in the EMI formula. The formula requires the monthly rate (annual rate / 12) and the monthly period count (years × 12). Using the annual rate produces an EMI roughly 12× too large; the error is obvious immediately but appears in spreadsheets where the formula has been copied without attention to unit consistency.
- Comparing loans by EMI rather than by total interest cost. A longer-term loan has a lower EMI but a higher total interest cost; choosing the lowest EMI without considering the longer payment term means paying more interest over the loan's life. A £200k mortgage at 5.5% costs £168k in interest over 25 years, £214k over 30 years, and £130k over 20 years — choose the term based on cash-flow capacity and total interest preference together, not EMI alone.
Frequently asked questions
What is EMI?
EMI stands for Equated Monthly Instalment — the fixed monthly payment that repays a loan over a stated term at a stated interest rate. Each EMI is identical in amount, but the split between interest and principal changes over the loan term: early payments are mostly interest, late payments are mostly principal. EMI is the standard repayment structure for mortgages, car loans, and personal loans worldwide.
How does the EMI formula work?
The formula EMI = P × r × (1+r)^n / ((1+r)^n − 1) computes the constant payment required to amortise the principal to zero over n monthly periods at monthly rate r. The numerator P × r × (1+r)^n represents the future-valued principal accumulating at compound interest; the denominator (1+r)^n − 1 normalises it back into a per-period payment. Algebraically, it solves the equation "what payment, paid n times into a sinking fund earning rate r, exactly equals the principal compounded forward at rate r?".
How is EMI different from interest cost?
EMI is the per-month cash payment; interest cost is the cumulative interest paid over the loan's life (EMI × n − principal). A £200k mortgage at 5.5% over 25 years has an EMI of £1228 but a total interest cost of £168k — over 80% of the principal again, paid over time. Lower EMI on a longer-term loan looks attractive in cash-flow terms but increases the total interest. The sensible decision balances monthly affordability against total cost.
What is amortisation?
Amortisation is the process by which a constant payment progressively repays the loan principal alongside accruing interest. Early in the loan, the outstanding balance is high so most of the EMI goes to interest; as the balance shrinks, more of each EMI goes to principal. The amortisation schedule is the month-by-month breakdown of interest, principal, and remaining balance for each EMI. Mortgage providers usually publish this on request; the calculator displays the year-end balance projection.
Why is the early portion of my mortgage mostly interest?
Because each month's interest is calculated as r × outstanding_balance, and in the first month the outstanding balance is the entire principal. For a £200k mortgage at 5.5%, the first month's interest is 200000 × (0.055/12) = £917; with an EMI of £1228, only £311 goes to principal. By month 240 (year 20) the outstanding balance has fallen to about £56k, so monthly interest is £257 and £971 of the EMI goes to principal — the ratio reverses entirely. The cumulative effect over a 25-year mortgage is that interest dominates the first half and principal dominates the second.