Quick Summary: The EMI formula looks complicated but is actually very logical. It calculates how much you need to pay each month so that your loan is fully repaid with interest by the end of the tenure. You only need three numbers: loan amount, interest rate, and tenure.
The Full EMI Formula
EMI = P x R x (1+R)^N
divided by [(1+R)^N - 1]
divided by [(1+R)^N - 1]
What Each Letter Means
- P (Principal) = The amount of money you are borrowing
- R (Monthly Rate) = Annual interest rate divided by 12 divided by 100
- N (Number of Payments) = Loan tenure in years multiplied by 12
- ^ (Power/Exponent) = Multiply the number by itself N times
Step-by-Step Calculation: $100,000 Loan at 10% for 5 Years
Step 1: Identify your values
- P = $100,000
- Annual rate = 10%, so R = 10 / 12 / 100 = 0.008333
- N = 5 years x 12 = 60 months
Step 2: Calculate (1+R)^N
(1 + 0.008333)^60 = (1.008333)^60 = 1.6453
Step 3: Calculate the numerator
P x R x (1+R)^N = 100,000 x 0.008333 x 1.6453 = 1,371
Step 4: Calculate the denominator
(1+R)^N - 1 = 1.6453 - 1 = 0.6453
Step 5: Divide to get EMI
EMI = 1,371 / 0.6453 = $2,125 per month
Quick Reference Table
| Loan Amount | Rate | 5 Years | 10 Years | 20 Years |
|---|---|---|---|---|
| $50,000 | 8% | $1,014 | $607 | $418 |
| $100,000 | 10% | $2,125 | $1,322 | $965 |
| $250,000 | 9% | $5,188 | $3,167 | $2,250 |
| $500,000 | 8% | $10,138 | $6,066 | $4,183 |
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