Money & everyday · 3 min read
Loan EMI Formula Explained: How Monthly Payments Are Calculated
The variables
- P = amount borrowed
- r = monthly rate = annual rate ÷ 12 ÷ 100
- n = number of monthly payments
- M = equal monthly payment
Example 1: 10,000 at 12% for 12 months
r = 0.01, n = 12. (1.01)¹² = 1.126825, so M = 10,000 × 0.01 × 1.126825 ÷ (1.126825 − 1) = 888.49. Total paid = 10,661.85, so interest is 661.85.
Example 2: 20,000 at 6% for 5 years
r = 0.005, n = 60: M = 386.66. Total paid 23,199.36; interest 3,199.36.
| Term | Monthly payment | Total interest |
|---|---|---|
| 36 months | 608.44 | 1,903.79 |
| 48 months | 469.70 | 2,545.63 |
| 60 months | 386.66 | 3,199.36 |
| 72 months | 331.46 | 3,864.96 |
A longer term lowers the payment but increases total interest.
Notes
Reproduce the arithmetic with the scientific calculator and learn the maths behind it in compound interest.
Frequently asked questions
What does EMI stand for?
Equated monthly instalment — the fixed payment each month.
Why is more of the early payment interest?
Interest is calculated on the outstanding balance, which is largest at the start.
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