EMI Calculator
From loan principal, annual rate and term, compute the fixed monthly instalment (EMI), total repayment and total interest — for personal loans, car loans and instalment plans.
Input Data
Results
At a glance:EMI (Equated Monthly Instalment) is a fixed monthly loan payment, widely used for mortgages, personal loans, car loans and instalments. It spreads principal and interest evenly so the monthly amount stays constant. Monthly payment = principal × monthly rate × (1+monthly rate)^n ÷ ((1+monthly rate)^n − 1); total payment = monthly × n; total interest = total − principal.
Formula
Monthly rate = annual rate ÷ 12; n = years × 12.
EMI = principal × monthly rate × (1+monthly rate)^n ÷ ((1+monthly rate)^n − 1).
Total payment = EMI × n; total interest = total payment − principal.
$$$EMI = P\\cdot\\dfrac{i(1+i)^{n}}{(1+i)^{n}-1}$$$$$$i=\\dfrac{\\text{Annual rate}}{12}$$n=\\text{Term (years)}\\times12$$$$$$Interest = EMI\\times n - P$$$How to Use
- Enter the loan principal.
- Enter the annual rate and term.
- View the fixed monthly payment (EMI), total repayment and total interest.
EMI and total interest at principal HK$500,000, 6% under different terms
| Term | Monthly (HK$) | Total (HK$) | Total interest (HK$) |
|---|---|---|---|
| 5 yr (60) | 9,666.40 | 579,984.05 | 79,984.05 |
| 10 yr (120) | 5,551.03 | 666,123.01 | 166,123.01 |
Case Studies
Case 1: Compute a loan's monthly payment
Borrow HK$500,000 at 6% for 5 years (60 periods). Monthly rate = 6% ÷ 12 = 0.5%, n = 60.
EMI = 500,000 × 0.005 × (1.005)^60 ÷ ((1.005)^60 − 1) ≈ HK$9,666.40; total = 9,666.40 × 60 ≈ HK$579,984; interest = 579,984 − 500,000 ≈ HK$79,984.
Interpretation: this loan costs a fixed HK$9,666/month, about HK$580k over 5 years, HK$80k of which is interest. The fixed payment works because early payments are interest-heavy and principal-light; as the balance falls, interest shrinks and principal grows, but the total stays constant.
Case 2: Longer term lowers the payment, at the cost of much more interest
Same HK$500,000 at 6%, extend the term from 5 to 10 years (120 periods). Monthly payment falls to about HK$5,551 (over 40% lower than 9,666) — cash-flow pressure eases clearly.
But total = 5,551 × 120 ≈ HK$666,123, interest ≈ HK$166,123 — more than double the 5-year plan's ~HK$80k.
Interpretation: extending the term eases the monthly burden but costs more in total interest because you borrow longer. Weigh monthly affordability against total interest cost; pick a shorter term if you can. Hong Kong mortgage actual payments also depend on bank rates (H/P plan) and stress tests; this is for estimation.
FAQ
What is EMI and why can the monthly payment stay fixed?
EMI (Equated Monthly Instalment) is a repayment where the monthly amount is the same throughout the term, also called amortisation. Interest is charged on the remaining principal, which is large early (more interest) and small later (less interest) — so why is the payment constant? EMI skilfully adjusts the principal/interest split each period: each fixed payment covers this period's interest (prior balance × monthly rate) plus some principal. Early on the balance is large so interest is high and principal share is low; as the balance falls, interest shrinks and principal share grows. The two offset so the total (EMI) stays fixed. The fixed amount is solved from the annuity formula so the balance hits zero exactly at term end. This calculator gives that monthly payment plus total and interest.
How are total payment and total interest computed? Why does a longer term cost more?
Once EMI is known: total payment = EMI × n (term × 12); total interest = total − principal (the extra you pay, i.e. the borrowing cost). Borrow 500,000 at 6% for 5 years: EMI ≈ 9,666.4, total ≈ 579,984, interest ≈ 79,984. Key point often missed: lengthening the term lowers the monthly payment but usually raises total interest a lot. EMI spreads principal and interest over more periods, so each payment is lower but you owe longer and accumulate more interest. Same 500,000 at 6% over 10 years drops the monthly payment clearly but total interest rises sharply (try term 10 here). So pick the term by both affordability and total interest — prefer a shorter term if you can, or prepay when allowed and penalties are low.
What to watch, and how is it related to a mortgage calculator?
This calculator uses the standard amortisation formula to estimate personal/car/instalment EMIs, but note: (1) the math is identical to a mortgage's monthly payment — a mortgage IS an EMI loan secured on property; this file is the general version while a mortgage calculator adds down payment, LTV and stress test. Results match for the same inputs. (2) Rate definition matters — we use nominal annual ÷ 12 (monthly compounding). Lenders may quote APR or a 'flat rate' (flat rate); flat rate differs from this reducing-balance rate and is usually far costlier at the same number. Compare by the lender's APR. (3) Fees excluded — handling, origination, insurance, late and early-repayment penalties are not counted, so real cost exceeds this interest. (4) Fixed-rate assumed; floating rates change payments. (5) Rounding to 2 decimals may differ minutely from the lender's schedule. Use it to estimate and compare combinations, not as a formal quote. Borrow within your means; terms and fees per the contract.
Does partial early repayment save interest? How does EMI change?
Yes — interest is on the remaining principal, so repaying principal earlier cuts future interest, most effective early (when the balance and interest share are large). After a partial prepayment, two common treatments: (1) keep the same EMI, shorten the term — you clear the loan sooner, usually the most interest saved; (2) recompute a lower EMI on the smaller balance, easing cash flow but keeping the term. Both save interest (principal reduced early); choose by whether you want to finish early or lower payments. Cautions: some loans have early-repayment penalties/lock-in — check if still worthwhile after the penalty; keep enough emergency cash; and weigh prepaying vs investing at a higher return than the loan rate. This calculator fixes EMI at given inputs; to test prepayment, re-enter the reduced balance and remaining term.
Relationship to a mortgage calculator — can I use it for a Hong Kong mortgage?
The core math is the same — a mortgage is a long-term secured loan whose monthly payment uses the EMI formula, so yes, enter the loan amount (price minus down payment), annual rate and term to estimate a mortgage's EMI, total and interest. But for a real Hong Kong mortgage, differences apply: (1) rate structure — H-plan (HIBOR + spread, with a P-plan cap) and P-plan (prime minus spread) float with the market, while this calculator uses one fixed rate for estimation only; (2) stress test and debt-servicing ratio — banks require passing the HKMA stress test and DS R ratio cap, affecting how much you can borrow; (3) other costs — legal fees, stamp duty, valuation, mortgage insurance (high-LTV) are outside EMI; (4) LTV cap sets down payment and loan size. Use this EMI calculator for a quick estimate of EMI/interest at a given rate and term, great for early planning and comparing terms; for the actual mortgage, rely on the bank's formal quote. For formal Hong Kong planning, also use a dedicated mortgage calculator with stress test and H/P plans. Estimation only, not advice.
Related Tools
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.