EMI Calculator - Equated Monthly Installment Loan Payment Calculator

Detailed Amortization Schedule

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

References

• Consumer Financial Protection Bureau - Understanding Loan Estimates
• FDIC - Smart Borrowing
• USA.gov - Loans and Credit
• Federal Reserve - Consumer Credit FAQs
• U.S. Department of Treasury - Interest Rate FAQs