Loan Payment Formula: How to Calculate Your Monthly Payment
The monthly payment on a fixed-rate loan is M = P × r(1 + r)^n / [(1 + r)^n − 1]. Here P is the amount you borrow, r is the monthly interest rate (the annual rate divided by 12), and n is the number of monthly payments. Plug in those three numbers and you get the level payment that pays the loan off to zero on the last due date. Below you will find each piece explained, four worked examples, and the amortization math that shows where every dollar goes.
TL;DR
- The formula is M = P × r(1 + r)^n / [(1 + r)^n − 1], with r = annual rate ÷ 12 and n = years × 12.
- A $32,000 loan at 6% over three years comes to about $973.50 a month, principal and interest only.
- Early payments are mostly interest. As the balance falls, more of the same payment goes to principal.
- The formula leaves out taxes, insurance and fees, so your real bill on a mortgage can be higher.
- You can check any result with our loan payment calculator.
Table of Contents
- The formula and what each letter means
- Step by step: how to calculate a loan payment
- Worked example 1: a $32,000 loan at 6% for three years
- Worked example 2: a $200,000 loan at 5% for 30 years
- Worked example 3: how much is a $20,000 loan per month?
- Worked example 4: $100,000 and $200,000 at other rates
- How amortization splits each payment
- When the standard formula needs adjusting
- Common mistakes
- Doing it in a spreadsheet or calculator
- Using the formula to make better decisions
- Perspective
- Check your numbers with our calculators
- FAQ
- Sources
The formula and what each letter means
The standard version for a fixed-rate, fully amortizing loan is [M = P × [r(1 + r)^n] / [(1 + r)^n − 1]](https://www.chase.com/personal/mortgage/education/financing-a-home/loan-amortization). Different sites write it with different letters (A, PMT, J, N), but the structure is the same.
| Symbol | Meaning | How you get it |
|---|---|---|
| M | Monthly payment | The answer you are solving for |
| P | Principal | The amount borrowed, as a dollar figure |
| r | Monthly interest rate | Annual rate as a decimal, divided by 12 |
| n | Number of payments | Term in years multiplied by 12 |
The annuity version
You will also see the formula written the other way around. OpenStax's finance textbook treats a loan as the present value of an annuity: the principal equals the payment multiplied by [1 − 1/(1 + r)^n] / r. Solve that for the payment and you get the same result as the formula above. Some people prefer this form because it reads as a single idea: the stream of equal payments, discounted at the loan rate, must equal what you borrowed today.
A third way to write it, which you will meet in some textbooks, is M = P × r / [1 − (1 + r)^−n]. It is the same formula with the numerator and denominator divided by (1 + r)^n. If your result differs from one source to another, check that you are using the same r and n rather than suspecting the formula.
Step by step: how to calculate a loan payment
- Write down the three inputs. Loan amount, annual interest rate and term in years.
- Convert the rate. Turn the annual percentage into a decimal (6% becomes 0.06), then divide by 12. For monthly payments, OpenStax says to divide the annual rate by 12, which gives 0.005 for 6%.
- Convert the term. Multiply years by 12. Three years is 36 payments, and 30 years is 360.
- Raise (1 + r) to the power n. This is the growth factor the loan balance would have if you never paid anything. On a calculator, use the y^x or ^ key.
- Build the fraction. Multiply r by that factor for the top, and subtract 1 from the factor for the bottom.
- Multiply by P. The result is your monthly payment. Round to the nearest cent.
Worked example 1: a $32,000 loan at 6% for three years
This is the example OpenStax uses, and it is a good one to practice on because the numbers are clean.
- P = 32,000
- r = 0.06 ÷ 12 = 0.005
- n = 3 × 12 = 36
The growth factor (1.005)^36 is about 1.19668. So:
M = 32,000 × 0.005 × 1.19668 ÷ (1.19668 − 1)
The top is about 191.47 and the bottom is about 0.19668, which gives roughly $973.50 a month. OpenStax reports the same figure, and notes that it excludes taxes, fees and other extras.
Over 36 payments you would pay about $35,046 in total, so the loan costs about $3,046 in interest.
Worked example 2: a $200,000 loan at 5% for 30 years
Here r = 0.05 ÷ 12 ≈ 0.0041667 and n = 360. Chase's loan amortization guide gives about $1,073.64 a month for this loan. Multiply by 360 and you pay roughly $386,510 in total, which means interest alone is close to $186,500, nearly as much as the amount borrowed.
That gap is why the term matters so much. Spreading principal repayment over more years lowers the payment, but you pay interest on a larger balance for longer.
Worked example 3: how much is a $20,000 loan per month?
This is a common personal loan size. Using the same steps at 7% annual interest:
| Term | n | r | Monthly payment | Total interest |
|---|---|---|---|---|
| 3 years | 36 | 0.005833 | about $617.54 | about $2,231 |
| 5 years | 60 | 0.005833 | about $396.02 | about $3,761 |
Worked example 4: $100,000 and $200,000 at other rates
Readers often ask what a $100,000 loan or a $200,000 loan at 7% costs. Using the formula on a 30-year term:
- $100,000 at 6% (r = 0.005, n = 360): about $599.55 a month.
- $200,000 at 7% (r ≈ 0.005833, n = 360): about $1,330.60 a month.
The second loan has a higher rate and the same term, and the payment is more than double the first even though the amount only doubled. Rate and amount compound each other.
To run your own numbers for a home purchase, try the mortgage payment calculator, which shows principal and interest for any price, rate and term.
How amortization splits each payment
The payment is level, but its contents change every month. The Chase guide explains that interest is calculated on the current balance, and whatever is left of the payment reduces principal. Early in the loan a larger share goes to interest. As the balance falls, the interest shrinks and more of the fixed payment goes to principal.
Here are the first two months of the $32,000 loan from example 1:
| Month | Starting balance | Interest (0.5%) | Principal paid | Ending balance |
|---|---|---|---|---|
| 1 | $32,000.00 | $160.00 | $813.50 | $31,186.50 |
| 2 | $31,186.50 | $155.93 | $817.57 | $30,368.93 |
Term versus amortization period
Two words that get mixed up. The amortization term is how long the rate and payment agreement stay unchanged/13%3A_Understanding_Amortization_and_its_Applications/13.01%3A_Calculating_Interest_and_Principal_Components), while the amortization period is how long it takes to reduce the principal to zero. On many home loans in other countries the two differ, for example a five-year term on a 25-year amortization schedule. On a typical fixed-rate U.S. loan they are the same.
When the standard formula needs adjusting
The formula assumes an ordinary amortizing loan: the first payment is due one period after you borrow, and every payment covers principal and interest. Several real situations change that.
Zero-interest loans
If r = 0, the formula divides zero by zero and fails. Skip it. The payment is simply P ÷ n. A $12,000 zero-percent loan over 24 months is $500 a month.
Variable and adjustable rates
Adjustable rates can move with economic conditions, which changes the payment per period. The practical method is to recalculate: take your current balance as P, the new rate as the annual rate, and the remaining number of payments as n. The result is your new payment.Balloon loans
A balloon loan typically has a much shorter term than the period used to calculate its monthly payments, which leaves a large final payment of the remaining balance. The formula still gives you the monthly figure, but you must plan for the lump sum at the end.
Taxes, insurance and fees
The formula returns principal and interest only. According to the CFPB, a mortgage's total monthly payment is often higher than the principal and interest payment because it often includes homeowners' insurance and taxes. Add those on top when you budget.
Payments at the start of the period
If the first payment is due on the day you borrow (common with some leases), you have an annuity due, and the payment is the ordinary result divided by (1 + r). Most consumer loans are ordinary, so you rarely need this.
Common mistakes
- Using the annual rate as r. Forgetting to divide by 12 gives a payment several times too high.
- Mixing years and months. If r is monthly, n must be months.
- Typing 6 instead of 0.06. Percent must become a decimal first.
- Rounding too soon. Keep at least six decimals in r until the last step.
- Comparing loans on payment alone. Always multiply the payment by n and subtract P to see total interest.
Doing it in a spreadsheet or calculator
Spreadsheets wrap the formula in a PMT function. For a $200,000 loan at 6.5% over 30 years, you would enter the monthly rate, the number of payments and the amount, and the sheet returns the payment as a negative number because it is cash going out. The mortgage calculator reference on Wikipedia shows this setup, along with the same annuity-based formula.
Once you know the payment, a tracking tool helps you stay on schedule. If you are juggling several balances, a debt payoff plan lays out an order for tackling them alongside your monthly figures.
Using the formula to make better decisions
The formula is not only for checking a lender's quote. A few ways to use it:
- Compare terms. Run the same loan at 3, 5 and 7 years to see payment and total interest side by side.
- Test the rate. A one-point rate difference on a large loan moves the payment by tens of dollars a month and thousands over the term.
- Plan extra payments. Paying more than M reduces principal faster, which cuts the interest charged each month. Our guide to extra mortgage payments shows how much that can save.
- Compare debts. Revolving debt works differently. See the credit card payoff formula for that case.
- Choose between paying off and investing. Our decision order for student loans versus investing puts the loan rate next to the alternative.
If you want to see how interest differs when it does not compound, the simple interest calculator and compound interest calculator make the contrast clear.
Perspective
We built MetriqaHub around a simple belief: a formula is only useful if you can check it in seconds and trust the answer. The loan payment formula looks intimidating on paper, yet it is three inputs and one fraction.>
Our approach is to show the math and then let the tool do the repetitive part. Work one example by hand so you understand why the payment is what it is, then use a calculator that follows the same standard formula for every other scenario. You get instant results with no registration, and you can change the rate or term as many times as you need.>
We also think the total-interest figure deserves more attention than it gets. The monthly payment decides whether you can afford a loan this month. The total cost decides whether it is the right loan. Looking at both before you sign is the habit we want our readers to build.>
Nkosi
Check your numbers with our calculators
You do not have to run the exponent by hand every time. Our free loan payment calculator gives you the monthly cost and interest for any amount, rate and term, instantly and without signing up. For the rest of our tools, from percentage change to savings growth, visit the MetriqaHub finance calculators.
FAQ
How do I calculate my loan payment?
Convert the annual rate to a monthly decimal (divide by 12), convert the term to months (multiply years by 12), then apply M = P × r(1 + r)^n / [(1 + r)^n − 1]. For $32,000 at 6% over three years, that gives about $973.50 a month.
How much is a $200,000 loan at 7%?
Over 30 years, the payment is about $1,330.60 a month for principal and interest. Over a shorter term the payment is higher but total interest is much lower. Property taxes and insurance would come on top for a mortgage.
What is the difference between the loan payment formula and the amortization formula?
The payment formula gives the fixed amount you pay each month. Amortization is the schedule that follows from it: each month interest is the balance times r, and the rest of the payment reduces principal until the balance reaches zero.
Does the formula work for a loan with no interest?
Not directly, because r = 0 makes the fraction undefined. Divide the loan amount by the number of payments instead. A $6,000 interest-free loan over 12 months is $500 a month.
Sources
- How do mortgage lenders calculate monthly payments? (Consumer Financial Protection Bureau)
- 8.3 Loan Amortization, Principles of Finance 2e (OpenStax)
- Amortized Loan: Definition, How to Calculate, Example (Chase)
- Calculating Mortgage Loans (Texas A&M Real Estate Research Center)
- 13.1: Calculating Interest and Principal Components (LibreTexts)/13%3A_Understanding_Amortization_and_its_Applications/13.01%3A_Calculating_Interest_and_Principal_Components)
- Paying Off Your Loans: Loan Amortization (Mississippi State University Extension)
- Mortgage calculator (Wikipedia)