EMI Calculator
Calculate equated monthly installments for loans.
EMI Calculator
($)
Year Month
(%)
Calculation Results
Total Interest
Month Payment
Total Payments
Amortization Schedule
| Month | Payments | Principal | Interest | Ending Balance |
|---|
| Year | Payments | Principal | Interest | Ending Balance |
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Payment Visualization
What Are the EMI Calculation Formulas?
Ordinary Annuity (Payment at End of Period)
When payments are made at the end of each period, the EMI is calculated using the following formula:
EMI = P × r × (1 + r)ⁿ / [(1 + r)ⁿ - 1]
Where:
- P = Principal loan amount
- r = Monthly interest rate (Annual Rate / 12 / 100)
- n = Total number of monthly payments (Loan term in months)
Annuity Due (Payment at Beginning of Period)
When payments are made at the beginning of each period, the formula adjusts to:
EMI = [P × r × (1 + r)ⁿ / [(1 + r)ⁿ - 1]] / (1 + r)
This results in slightly lower monthly payments since each payment has more time to reduce the principal before interest accrues.
Example Calculation
Given:
- Loan Amount (P) = $100,000
- Annual Interest Rate = 6%
- Monthly Interest Rate (r) = 6% / 12 = 0.5% = 0.005
- Loan Term = 3 years = 36 months (n)
For End-of-Period Payment:
EMI = 100,000 × 0.005 × (1.005)³⁶ / [(1.005)³⁶ - 1]
EMI = 100,000 × 0.005 × 1.1967 / [1.1967 - 1]
EMI = 598.35 / 0.1967
EMI ≈ $3,042.19
For Beginning-of-Period Payment:
EMI = [100,000 × 0.005 × (1.005)³⁶ / [(1.005)³⁶ - 1]] / 1.005
EMI = [100,000 × 0.005 × 1.1967 / [1.1967 - 1]] / 1.005
EMI = [598.35 / 0.1967] / 1.005
EMI ≈ $3,027.06
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