Loan Calculator

Monthly Loan Payment Estimator

Loan Monthly Payment Formula

Formula

\[ M = \frac{P \times r}{1 - (1 + r)^{-n}} \]

Where:

$M$ — monthly payment
$P$ — loan principal (the amount borrowed)
$r$ — monthly interest rate (annual rate divided by 12)
$n$ — total number of monthly payments (loan term in years multiplied by 12)

This is the standard amortizing loan formula: it produces a fixed payment that pays off both interest and principal completely over the term. If the interest rate is 0%, the payment is simply $M = P / n$.

Loan Calculator – Calculation Example

Example: you borrow $200,000 at an annual interest rate of 5% for a 30-year term.

\[ r = \frac{5\%}{12} = 0.0041667, \quad n = 30 \times 12 = 360 \text{ months} \]

\[ M = \frac{200{,}000 \times 0.0041667}{1 - (1 + 0.0041667)^{-360}} = \frac{833.33}{0.776169} \approx 1{,}073.64 \]

Result: the monthly payment is $1,073.64. Over 360 payments, the total payment is $386,510.40, of which $186,510.40 is interest — you can reproduce these numbers with the calculator's default values.

How to Use the Loan Calculator

Enter the Loan Amount (P) — the principal you plan to borrow, in dollars.
Enter the Annual Interest Rate as a percentage (for example, enter 5 for 5%, or 5.25 for 5.25%).
Enter the Loan Term (years) — the number of years over which you will repay the loan.
Read the results: the calculator shows the Monthly Payment, the Total Payment (principal plus all interest), and the Total Interest you will pay over the life of the loan.

What Is an Amortizing Loan?

Most consumer loans — mortgages, auto loans, personal loans, and student loans — are amortizing loans. You make identical payments every month, but the split between interest and principal changes over time. Early in the loan, when the outstanding balance is largest, most of each payment covers interest. As the balance shrinks, a growing share of the payment goes toward principal, until the debt is fully repaid in the final month.

The monthly payment calculated above stays constant for the entire term (assuming a fixed interest rate). That predictability is what makes amortizing loans easy to budget around: you know exactly what leaves your bank account each month.

The Total Interest figure is often the most eye-opening result. In the default example, a $200,000 loan at 5% for 30 years costs over $186,000 in interest — nearly as much as the principal itself. Shortening the term or securing a lower rate dramatically reduces this figure, which is why comparing loan offers matters so much.

How to Interpret the Results

Use the monthly payment to check affordability: a common guideline is that total debt payments should stay below roughly a third of your gross monthly income. The total interest tells you the true cost of borrowing, not just the sticker price of what you are financing.

Experiment with the inputs to see cause and effect. Doubling the term lowers the monthly payment but can more than double the total interest. Even a 0.5% difference in the interest rate can shift the total cost by thousands of dollars over a long loan.

Assumptions and Limitations

Fixed rate only. The calculator assumes the interest rate never changes. Variable-rate loans (ARMs, some private student loans) will have different payments once the rate adjusts.
No fees included. Origination fees, closing costs, points, and insurance are not part of the result. For mortgages, property taxes and homeowners insurance are typically added on top — see the Mortgage Calculator for a fuller picture, or the Mortgage APR Calculator to compare rates with fees included.
Monthly compounding. The formula converts the annual rate to a monthly rate by dividing by 12, which matches how most consumer loans in the US accrue interest.
No extra payments. The result assumes you pay exactly the scheduled amount every month. Paying extra toward principal shortens the loan and cuts total interest (watch out for a possible pre-payment penalty).

Practical Tips

Run the numbers for several terms (15 vs. 30 years for a mortgage, 36 vs. 60 months for a car) to find the balance between an affordable payment and total cost.
For vehicle financing specifically, the Auto Loan Calculator lets you fine-tune the same trade-off.
Before committing, use the result to negotiate: knowing your exact payment at a given rate makes it easier to compare lender offers on equal terms.

Frequently Asked Questions

What is a good interest rate on a loan?

There is no single "good" rate — it depends on the loan type, your credit score, and market conditions. Mortgages usually carry the lowest rates, auto loans sit in the middle, and unsecured personal loans are the highest, because the lender takes more risk. As a rule of thumb, the stronger your credit history and the shorter the term, the lower the rate you will be offered. Always compare several quotes in writing before signing.

What is the difference between interest rate and APR?

The interest rate determines your monthly payment, while the APR (annual percentage rate) also folds in lender fees, points, and some closing costs, expressed as a yearly percentage. Two lenders can quote the same interest rate but different APRs — the one with the lower APR is usually cheaper overall. Use the interest rate in this calculator for the payment amount, and the APR to compare total loan offers.

How do I calculate the remaining balance after some years of payments?

The balance after $k$ payments is $B = P(1+r)^k - M\frac{(1+r)^k - 1}{r}$, where $P$ is the original principal, $r$ the monthly rate, and $M$ your monthly payment. For example, after 5 years of the default loan, the balance is still around $186,000 — early payments barely dent the principal. This is also why selling or refinancing early in a long loan returns less equity than people expect.

Does making biweekly payments instead of monthly save money?

Yes, indirectly. Biweekly half-payments mean you make 26 half-payments per year — the equivalent of 13 full monthly payments — so you pay one extra month each year. On a 30-year mortgage that typically cuts about 4–6 years off the term and saves tens of thousands in interest. The interest math itself is unchanged; the savings come purely from the accelerated payoff. Check that your lender applies extra amounts to principal.

Why is my total interest almost as large as the loan itself?

Interest accumulates on the outstanding balance every month for the entire term, so long loans at moderate rates can cost nearly as much in interest as the principal. On the default example, a $200,000 loan at 5% for 30 years accrues about $186,000 in interest. Shortening the term attacks this directly: the same loan over 15 years costs roughly $85,000 in interest — less than half — though the monthly payment rises substantially.

Why does my actual lender payment differ slightly from the calculator result?

Common reasons include fees rolled into the loan, rounded payment amounts, a first payment date that is more or less than a month away, or a rate quoted with more decimal places. Mortgages also usually add escrow amounts for property taxes and insurance on top of principal and interest, which this calculator deliberately excludes. Treat the result as a close estimate of principal-and-interest only, not the final number on your statement.

How much does one extra payment per year save on my loan?

It depends on the rate and term, but the effect is large on long loans. Adding a single extra monthly payment each year on a 30-year, 5% mortgage shortens the payoff by roughly 4–5 years and saves 20–30% of the total interest. Extra payments go entirely to principal, which shrinks the balance that future interest is charged on. Confirm your loan has no prepayment penalty before doing this.