Loan Calculator
Calculate monthly payments, total interest and total cost for any personal loan.
Quick Answer
A fixed-rate loan payment is calculated with M = P[r(1+r)^n]/[(1+r)^n-1], where P is the loan amount, r is the monthly interest rate (APR/12), and n is the total number of monthly payments. This is the standard amortization formula used by the Consumer Financial Protection Bureau.
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How Loan Payments Are Calculated
When you borrow money, the lender expects you to repay the principal (the amount borrowed) plus interest (the cost of borrowing) over a defined period. Most consumer and commercial loans use a fully amortizing structure, which means every monthly payment is the same dollar amount from the first month to the last. Each payment is split into two parts: one portion covers the interest that accrued on the outstanding balance during the previous month, and the remainder reduces the principal. Because the balance shrinks with every payment, the interest portion decreases over time while the principal portion increases, even though the total payment stays constant.
The size of each payment depends on three variables: the loan amount, the annual interest rate, and the number of payments (the term). Change any one of these and the payment changes. A higher rate or shorter term increases the payment; a lower rate or longer term decreases it. Fixed-rate loans lock in the interest rate for the entire term, making your budget predictable. Variable-rate (or adjustable-rate) loans tie the rate to a benchmark such as the prime rate or SOFR index, so the payment can rise or fall when the benchmark moves. Most personal loans, auto loans, and conventional mortgages use fixed rates, while home equity lines of credit (HELOCs) and some student loans use variable rates.
Understanding the amortization process is critical because it reveals how much of your early payments go toward interest versus principal. On a 30-year mortgage, for example, more than 70% of each payment in the first year goes to interest. This is why making even small extra principal payments early in the loan term can save thousands of dollars in interest over the life of the loan. Every dollar of early principal reduction prevents interest from accruing on that amount for the remaining term, creating a compounding savings effect.
Loan Payment Formula
The standard formula for calculating the fixed monthly payment on an amortizing loan is:
M = P × [r(1 + r)n] / [(1 + r)n − 1]
Where:
- M = monthly payment
- P = principal (the amount borrowed)
- r = monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = total number of payments (loan term in months)
This formula assumes a fixed rate and equal monthly payments. If the annual rate is 0%, the formula simplifies to M = P / n. For variable-rate loans, lenders recalculate the payment whenever the rate adjusts, using the remaining balance as the new principal and the remaining months as the new term. Interest-only loans use a simpler formula (M = P × r) during the interest-only period, after which the loan re-amortizes over the remaining term at the fully amortizing payment.
Worked Example: $200,000 at 6% for 15 Years
- Step 1: Convert the annual rate to a monthly rate: r = 6% ÷ 12 ÷ 100 = 0.005
- Step 2: Calculate total payments: n = 15 × 12 = 180
- Step 3: Compute (1 + r)n = (1.005)180 = 2.45409
- Step 4: Plug into the formula: M = $200,000 × [0.005 × 2.45409] / [2.45409 − 1]
- Step 5: M = $200,000 × 0.012270 / 1.45409 = $200,000 × 0.008439 = $1,687.71/month
- Total repaid over 15 years: $1,687.71 × 180 = $303,788
- Total interest paid: $303,788 − $200,000 = $103,788
Key Loan Terms Explained
- Principal: The original amount you borrow. As you make payments, the outstanding principal decreases. Your interest each month is calculated on this remaining principal balance, which is why paying extra toward principal saves interest over the life of the loan.
- Interest Rate: The annual percentage the lender charges on the outstanding principal. A 6% rate means you pay 6 cents per year for every dollar owed. The rate is divided by 12 to compute monthly interest. Rates vary based on creditworthiness, loan type, and current market conditions.
- APR (Annual Percentage Rate): A broader measure of borrowing cost that includes the interest rate plus fees such as origination charges, discount points, and closing costs, expressed as a yearly rate. Federal law (Truth in Lending Act) requires lenders to disclose APR so borrowers can compare offers on equal footing. The APR is always equal to or higher than the nominal interest rate.
- Term: The length of the repayment period, usually stated in months or years. Common terms are 36, 48, or 60 months for auto and personal loans and 15 or 30 years for mortgages. A shorter term means higher monthly payments but significantly less total interest paid over the life of the loan.
- Amortization: The process of spreading loan repayment across a series of fixed periodic payments. Each payment covers interest first, then principal. An amortization schedule is the month-by-month table showing this breakdown, letting you track how quickly your balance declines and how much interest you pay each month.
- Balloon Payment: Some loans have lower regular payments but require a large lump-sum payment at the end of the term. This structure is common in commercial real estate and some auto financing. Borrowers must plan to refinance or pay the balloon when it comes due, which introduces refinancing risk.
- Prepayment Penalty: A fee some lenders charge if you pay off the loan ahead of schedule. The penalty compensates the lender for lost interest income. Before signing, check whether your loan includes a prepayment penalty and how it is calculated, as it can offset the savings from paying early.
Fixed vs. Variable Rate Comparison
Choosing between a fixed and variable rate affects your payment predictability, total cost, and risk exposure. The table below summarizes the key differences to help you decide which structure fits your situation.
| Feature | Fixed Rate | Variable Rate |
|---|---|---|
| Interest Rate | Stays the same for the entire term | Changes periodically with a benchmark index (e.g., SOFR, Prime) |
| Monthly Payment | Constant and predictable every month | Can increase or decrease at each adjustment |
| Initial Rate | Usually higher than initial variable rate | Often lower introductory rate for first 1-5 years |
| Risk | No rate risk; total cost is known upfront | Payment can rise significantly if rates increase |
| Best For | Long-term loans; borrowers who want certainty | Short-term loans; borrowers expecting rate drops |
| Common Examples | Conventional mortgages, auto loans, personal loans | HELOCs, adjustable-rate mortgages (ARMs), some student loans |
Types of Loans Compared
Different loan products serve different purposes and carry different rate ranges, terms, and requirements. The table below provides a general comparison of the most common loan types available to consumers.
| Loan Type | Typical Rate | Typical Term | Secured? | Best For |
|---|---|---|---|---|
| Mortgage | 5.5%–7.5% | 15 or 30 years | Yes (home) | Home purchase or refinance |
| Auto Loan | 4.5%–10% | 36–72 months | Yes (vehicle) | New or used car purchase |
| Personal Loan | 6%–24% | 12–60 months | No | Debt consolidation, home improvement, medical bills |
| Student Loan (Federal) | 5%–8.5% | 10–25 years | No | College tuition, books, living expenses |
| Home Equity Loan | 6%–10% | 5–30 years | Yes (home) | Large expenses using home equity |
Practical Examples
Scenario 1: $15,000 Personal Loan at 9% for 3 Years
- Monthly rate: 9% ÷ 12 = 0.75% (0.0075)
- Total payments: 3 × 12 = 36
- Monthly payment: $477.00
- Total interest: $2,172. Total repaid: $17,172
A 3-year term keeps total interest relatively low at about 14.5% of the original loan amount. This is a common choice for debt consolidation or a home improvement project. Adding just $50 per month extra toward principal would pay off the loan 3 months early and save approximately $150 in interest.
Scenario 2: $30,000 Auto Loan at 5.5% for 5 Years
- Monthly rate: 5.5% ÷ 12 = 0.4583% (0.004583)
- Total payments: 5 × 12 = 60
- Monthly payment: $573.19
- Total interest: $4,391. Total repaid: $34,391
Auto loans tend to carry lower rates than unsecured personal loans because the vehicle serves as collateral. A 60-month term balances affordable payments against reasonable total interest. Shortening to 48 months raises the payment to $698 but saves $1,072 in interest.
Scenario 3: $250,000 Mortgage at 6.5% for 30 Years
- Monthly rate: 6.5% ÷ 12 = 0.5417% (0.005417)
- Total payments: 30 × 12 = 360
- Monthly payment: $1,580.17
- Total interest: $318,861. Total repaid: $568,861
Over 30 years the total interest exceeds the original principal. Switching to a 15-year term at the same rate raises the payment to $2,177 but cuts total interest to $141,862, saving $176,999. Use our Mortgage Calculator for more detailed home loan analysis.
How to Reduce Your Monthly Payment
If your current loan payment feels too high, or you want to minimize payments on a new loan, consider these proven strategies:
- Choose a longer term: Extending from 15 to 30 years on a mortgage, or from 36 to 60 months on a personal loan, spreads the principal over more payments and lowers each one. The trade-off is significantly more total interest paid over the life of the loan. Use the calculator above to see the exact impact on both your monthly payment and total cost.
- Secure a lower interest rate: Even a 0.5% rate reduction on a $200,000 loan saves roughly $60 per month and over $20,000 in total interest over 30 years. Improve your credit score before applying, shop multiple lenders, and consider paying discount points to buy down the rate at closing.
- Refinance an existing loan: If market rates have dropped since you took out your loan, refinancing at a lower rate can meaningfully reduce your payment. Factor in closing costs and fees to confirm the break-even point makes refinancing worthwhile. Typically, a rate drop of at least 0.75% to 1% justifies refinancing costs.
- Make a larger down payment: Putting more money down upfront reduces the principal, which lowers both the monthly payment and total interest. On a home purchase, a 20% down payment also eliminates private mortgage insurance (PMI), saving an additional $100 to $300 per month on many loans.
- Consolidate multiple debts: Replacing several high-rate debts with a single lower-rate loan can reduce your combined monthly obligations and simplify your finances. A Debt Payoff Calculator can help you compare strategies.
Fixed Term vs. Fixed Payment Approach
When planning a loan, you can approach it from two angles. The fixed-term approach is the most common: you decide the loan amount, rate, and term, and the formula tells you the monthly payment. This is how the calculator above works. It answers the question, "How much will I pay each month if I borrow $X at Y% for Z years?"
The fixed-payment approach works in reverse. You start with a monthly payment you can comfortably afford and solve for the maximum loan amount or the shortest term. For example, if you can afford $500 per month and the rate is 7%, the formula tells you that you can borrow up to approximately $20,979 over 48 months, or about $29,880 over 72 months. This approach is useful for budgeting because it ensures your loan fits within your monthly cash flow before you start shopping for a car, home, or other financed purchase.
Financial advisors generally recommend that your total monthly debt payments (including the new loan) should not exceed 36% of your gross monthly income. This is known as the debt-to-income (DTI) ratio. Mortgage lenders in particular use DTI thresholds of 43% to 50% as qualification cutoffs. Using the fixed-payment approach helps you stay within these guidelines and avoid over-borrowing. If both approaches suggest a comfortable payment, you have strong confirmation that the loan is affordable and sustainable over the full term.