How Loan Repayment Works
When you take out a loan, you repay it through equal monthly instalments (EMI). Each payment covers the interest accrued that month plus a portion of the principal. This page explains the formula, how amortization works, and what affects the total cost of a loan.
The EMI Formula
| Symbol | Variable | Example value |
|---|---|---|
| M | Monthly payment (EMI) | $1,199.10 |
| P | Principal | $200,000 |
| r | Monthly rate = Annual ÷ 1200 | 0.005 (= 6% ÷ 12) |
| n | Total months = Years × 12 | 360 (= 30 years) |
How Amortization Works
Amortization is the process of paying off a debt over time through regular payments. Each payment is split into two parts:
- Interest portion: Outstanding balance × Monthly rate
- Principal portion: Monthly payment − Interest portion
Because the outstanding balance shrinks with each payment, the interest portion of each payment decreases over time, while the principal portion increases.
| Month | Opening Balance | Interest | Principal | Closing Balance |
|---|---|---|---|---|
| 1 | $200,000.00 | $1,000.00 | $199.10 | $199,800.90 |
| 2 | $199,800.90 | $999.00 | $200.10 | $199,600.80 |
| 60 | $186,108.50 | $930.54 | $268.56 | $185,839.94 |
| 180 | $140,430.20 | $702.15 | $496.95 | $139,933.25 |
| 360 | $1,193.13 | $5.97 | $1,193.13 | $0.00 |
Worked Example — 30-Year Mortgage
P = $200,000, Annual Rate = 6%, Term = 30 years
- Monthly rate: r = 6 ÷ 1200 = 0.005
- Total months: n = 30 × 12 = 360
- EMI = 200,000 × 0.005 × (1.005)^360 / ((1.005)^360 − 1)
Impact of Loan Term
A longer term lowers the monthly payment but dramatically increases total interest paid.
| Term | Monthly EMI | Total Paid | Total Interest |
|---|---|---|---|
| 10 years | $2,220.41 | $266,449 | $66,449 |
| 15 years | $1,687.71 | $303,788 | $103,788 |
| 20 years | $1,432.86 | $343,887 | $143,887 |
| 30 years | $1,199.10 | $431,676 | $231,676 |
Impact of Interest Rate
| Annual Rate | Monthly EMI (30 yr) | Total Interest (30 yr) |
|---|---|---|
| 3% | $843.21 | $103,554 |
| 4% | $954.83 | $143,739 |
| 5% | $1,073.64 | $186,511 |
| 6% | $1,199.10 | $231,676 |
| 8% | $1,467.53 | $328,311 |
| 10% | $1,755.14 | $431,850 |
Extra Payments
Making extra payments reduces the principal faster. Since future interest is calculated on a lower balance, total interest falls and the loan is paid off earlier.
- Loan Calculator — Calculate EMI and see the full amortization schedule
- Loan Formula — Full EMI formula reference with derivation and worked examples
Frequently Asked Questions
Why do I pay more interest at the start of a loan?
Because interest is charged on the outstanding balance. At the start, the balance is at its maximum, so the interest portion of each payment is largest. As the balance shrinks, less interest accrues each month and more of the fixed payment goes toward principal.
What happens if I miss a payment?
A missed payment usually incurs a late fee and the unpaid interest gets added to the outstanding balance, increasing future interest charges. Repeated missed payments can damage your credit score and eventually lead to default.
Is a shorter loan term always better?
Shorter terms save significant interest and build equity faster, but the higher monthly payments may strain cash flow. A longer term is sensible if the freed-up cash is invested at a return higher than the loan interest rate.
What is an amortization schedule?
An amortization schedule is a complete table showing every monthly payment, the interest and principal portions of each payment, and the remaining balance after each payment. It lets you see exactly how the loan is paid off month by month.