How it works
With equal payment (annuity) the amount you pay each month is the same; early payments are mostly interest and later ones mostly principal.
With equal principal you repay the same principal each month, so the payment starts higher and decreases over time. It costs less total interest but has a heavier early burden.
Monthly = P × r × (1+r)^n ÷ ((1+r)^n − 1), where r is the monthly rate and n the number of months.
This assumes a fixed rate with no grace period. Real loans may include fees, variable rates and early-repayment terms.
How do I calculate a loan payment?
To calculate a loan payment, multiply the principal by the monthly interest rate and by (1 + rate) raised to the power of the number of payments, then divide by that same factor minus 1. Example: a loan of 100,000 at 4.5% annual interest over 30 years (360 monthly payments) has a monthly payment of 506.69.
Steps to calculate a loan payment
- Convert the annual interest rate to a monthly rate: divide by 12, then by 100 (4.5% becomes 0.00375).
- Convert the loan term to months: multiply years by 12 (30 years becomes 360 months).
- Raise (1 + monthly rate) to the power of the number of months.
- Multiply the principal by the monthly rate and by that result.
- Divide by (that result minus 1) to get the monthly payment.
Loan payment formula
Monthly payment = P × r × (1 + r)^n ÷ ((1 + r)^n - 1)
- P = principal, the loan amount
- r = monthly interest rate (annual rate divided by 12 and by 100)
- n = number of monthly payments (years multiplied by 12)
Quick loan payment answers
What is the monthly payment on a 100,000 loan at 4.5% for 30 years?
The monthly payment is 506.69 (100,000 × 0.00375 × 1.00375^360 ÷ (1.00375^360 − 1)).
How much total interest do you pay on a 100,000 loan at 4.5% over 30 years?
Total interest is 82,406.71 over the 30-year term.
How much more is the payment if the rate rises from 4.5% to 5.5%?
The monthly payment rises from 506.69 to 567.79, an increase of 61.10.
What is the monthly payment on the same 100,000 loan at 4.5% over 15 years instead of 30?
Over 15 years the payment is 764.99, higher than the 506.69 30-year payment.
How much interest do you save by choosing a 15-year term instead of 30 years on that loan?
Total interest drops from 82,406.71 to 37,698.79, a saving of 44,707.92.
What is the monthly payment on a 100,000 loan at 6.0% for 30 years?
The monthly payment is 599.55.
What is the monthly payment on a 300,000 loan at 3.5% for 15 years?
The monthly payment is 2,144.65.
What is the monthly payment on a 30,000 loan at 5.0% for 5 years?
The monthly payment is 566.14.
Example monthly payments
| Loan amount | Rate | Term | Monthly payment | Total interest |
|---|
| 100,000 | 4.5% | 30 years | 506.69 | 82,406.71 |
| 100,000 | 4.5% | 15 years | 764.99 | 37,698.79 |
| 100,000 | 6.0% | 30 years | 599.55 | 115,838.19 |
| 300,000 | 3.5% | 15 years | 2,144.65 | 86,036.57 |
| 30,000 | 5.0% | 5 years | 566.14 | 3,968.22 |
Frequently asked questions
What is the difference between equal payment and equal principal?
Equal payment (annuity) keeps the monthly payment the same for the whole term; interest dominates early on and principal dominates later. Equal principal keeps the principal portion constant each month, so the payment starts higher and decreases over time, producing less total interest but a heavier early burden.
Does a lower interest rate always mean a lower monthly payment?
Yes. For the same principal and term, a lower rate always produces a lower monthly payment and less total interest, because both the numerator and denominator of the formula shrink together with the rate.
How does the loan term affect total interest?
A longer term lowers the monthly payment but increases total interest, since interest accrues on the outstanding balance for more months. In the table above, extending a 100,000 loan at 4.5% from 15 to 30 years raises total interest from 37,698.79 to 82,406.71.
Does this calculator include fees or taxes?
No. It calculates principal and interest only, assuming a fixed rate with no grace period. Real loans may include origination fees, insurance, property taxes, or a variable rate that changes the actual payment over time.
This calculator estimates payments from principal, a fixed annual rate and a term only. Actual loan terms such as fees, variable rates, early-repayment penalties or grace periods can change your real payment, so treat the result as reference and confirm the exact terms with your lender before signing.