Quick answer
Monthly payment formula: M = P × r(1+r)^n / [(1+r)^n − 1]. Example: $200,000 loan at 6% for 30 years = $1,199/month, total interest paid = $231,676.
How to use this calculator
Enter the Loan Amount (principal borrowed, not including interest), the Annual Interest Rate as a percentage, and the Loan Term in years. The calculator shows your fixed monthly payment covering principal and interest, the total amount paid over the life of the loan, total interest paid, and a year-by-year amortisation table.
For a mortgage, the loan amount is the purchase price minus your down payment. The calculator covers principal and interest only — property taxes, homeowner's insurance, and PMI are not included.
Loan payment formula
The standard formula for a fixed-rate amortising loan (used for mortgages, car loans, and personal loans) is:
$$M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$$
Where:
- M = fixed monthly payment
- P = principal (loan amount)
- r = monthly interest rate = annual rate ÷ 12
- n = total number of payments = years × 12
From the monthly payment, total paid and total interest are straightforward:
$$\text{Total Paid} = M \times n$$
$$\text{Total Interest} = \text{Total Paid} - P$$
If the interest rate is 0% (e.g., a 0% promotional loan), the payment simplifies to P ÷ n — just the principal divided by the number of months.
Worked examples
| Loan Type | Amount | Rate | Term | Monthly Payment | Total Interest |
|---|---|---|---|---|---|
| 30-year mortgage | $300,000 | 7.0% | 30 yr | $1,996 | $418,527 |
| 15-year mortgage | $300,000 | 6.5% | 15 yr | $2,613 | $170,285 |
| Car loan | $35,000 | 5.9% | 5 yr | $674 | $5,419 |
| Personal loan | $20,000 | 12.0% | 3 yr | $664 | $3,921 |
| Student loan | $50,000 | 6.5% | 10 yr | $567 | $18,007 |
How interest rate affects monthly payment
Interest rate has a direct and significant impact on monthly payment. The table below shows how a $300,000 30-year mortgage changes with different rates:
| Annual Rate | Monthly Payment | Total Interest | vs. 4% rate |
|---|---|---|---|
| 4.0% | $1,432 | $215,609 | — |
| 5.0% | $1,610 | $279,767 | +$64,158 |
| 6.0% | $1,799 | $347,515 | +$131,906 |
| 7.0% | $1,996 | $418,527 | +$202,918 |
| 8.0% | $2,201 | $492,349 | +$276,740 |
Each 1% increase in rate adds roughly $150–$200/month on a $300,000 mortgage and over $60,000–$80,000 in total interest over 30 years.
Loan term vs. total interest
A longer loan term reduces monthly payments but substantially increases total interest. On a $300,000 loan at 6.5%:
| Loan Term | Monthly Payment | Total Interest | Total Paid |
|---|---|---|---|
| 10 years | $3,406 | $108,691 | $408,691 |
| 15 years | $2,613 | $170,285 | $470,285 |
| 20 years | $2,237 | $236,856 | $536,856 |
| 25 years | $2,029 | $308,702 | $608,702 |
| 30 years | $1,896 | $382,574 | $682,574 |
Choosing a 15-year over a 30-year mortgage saves $212,289 in interest — despite the higher monthly payment. If you can comfortably afford the higher payment, a shorter term is almost always the better financial decision.
Types of loans this calculator covers
This calculator works for any fixed-rate amortising loan — a loan where the interest rate stays constant and each payment reduces the balance until it reaches zero at term end:
- Mortgages: 15-year and 30-year fixed-rate home loans are the most common application.
- Car loans: Typically 3–7 year terms at rates between 4% and 15% depending on credit score and vehicle age.
- Personal loans: Unsecured loans for debt consolidation, home improvement, or major purchases. Usually 2–7 years at higher rates than mortgages.
- Student loans: Federal student loans typically use standard 10-year repayment. Income-driven repayment plans use different terms.
- Business loans: Term loans from banks or SBA lenders with fixed rates.
This calculator does not apply to variable-rate loans, interest-only loans, balloon loans, or revolving credit (credit cards).
Frequently asked questions
What is the loan payment formula?
M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is principal, r is monthly rate (annual rate ÷ 12), and n is total months (years × 12). For $200,000 at 6% for 30 years: r = 0.005, n = 360, M = $1,199/month.
How do I calculate my monthly mortgage payment?
Enter the loan amount (purchase price minus down payment), the annual interest rate, and the term (usually 30 or 15 years). The result is your principal-and-interest payment. Add property taxes, insurance, and PMI separately to get your total monthly housing cost.
What is amortisation?
Amortisation is the process of paying off a loan through regular payments. Each payment covers interest on the remaining balance and reduces the principal. Early payments are mostly interest; later payments are mostly principal. By the last payment, the balance is exactly zero.
How does the loan term affect total interest?
A longer term means lower monthly payments but much more total interest. A $300,000 loan at 6.5% costs $170,285 in interest over 15 years versus $382,574 over 30 years — a difference of $212,289. The shorter term is nearly always cheaper if you can afford the higher payment.
What happens if I pay extra each month?
Extra principal payments directly reduce the outstanding balance, which reduces future interest charges and shortens the loan term. On a $200,000 30-year mortgage at 6.5%, an extra $200/month saves roughly $73,000 in interest and eliminates about 6 years of payments. Most fixed-rate loans allow prepayment without penalty — check your loan agreement.