What Is the Formula for a Monthly Loan Payment?

Image shows three characters using clipboards and calculators. Text reads: How to Calculate Your Monthly Payment on Interest-Only Loans. Monthly payment = a*(r/n) or (a*r)/12. Where “a” is amount borrowed, “r” is annual interest rate, and “n” is number of payments per year (12 for monthly). For example, you borrowed $100,000 at a6% interest rate: Calculation 1: $100,000*(0.06/12) = $500 monthly payment. Calculation 2: ($100,000*0.06)/12 = $500 monthly payments.

The Balance / Julie Bang


The monthly payment formulas calculate how much a loan payment will be and include the loan's principal and interest.

Definition and Examples of Monthly Loan Payments

When you receive a loan from a lender, you receive an amount called the principal, and the lender tacks on interest. You pay back the loan over a set number of months or years, and the interest makes the total amount of money you owe larger. Your monthly loan payments will typically be broken into equal payments over the term of the loan.

How you calculate your payments depends on the type of loan. Here are three types of loans you'll run into the most, each of which is calculated differently:

  • Interest-only loans: You don’t pay down any principal in the early years—only interest.
  • Amortizing loans: You're paying toward both principal and interest over a set period. For instance, a five-year auto loan might begin with 75% of your monthly payments focused on paying off interest, and 25% paying toward the principal amount. The amount you pay on interest and principal changes over the loan term, but your monthly payment amount does not.
  • Credit card loans: A credit card gives you a line of credit that acts as a reusable loan as long as you pay it off in time. If you're late making monthly payments and carry your balance to the next month, you'll likely be charged interest.

How Do You Calculate Monthly Loan Payments?

Since the payments on different types of loans focus on different balances, there are separate ways to calculate your monthly payments. Here's how to calculate the three types discussed previously.

Amortized Loan Payment Formula

Calculate your monthly payment (P) using your principal balance or total loan amount (a), periodic interest rate (r), which is your annual rate divided by the number of payment periods, and your total number of payment periods (n):

Amortization formula

Interest-Only Loan Payment Formula

Calculating payments for an interest-only loan is easier. First, divide the annual interest rate (r) by the number of payments per year (n), then multiply it by the amount you borrow (a):

Interest omnly formula

Credit Card Payment Calculations

Credit cards also use fairly simple math, but determining your balance takes more effort because it constantly fluctuates, and lenders charge different rates. They typically use a formula to calculate your minimum monthly payment based on your total balance. For example, your card issuer might require that you pay at least $25 or 1% of your outstanding balance each month, whichever is greater.

In that case, the formula you'd use would be:

Simple Interest Formula

How Do the Loan Payment Calculations Work?

To demonstrate the difference in monthly payments, here are some working examples to help you get started.

Amortization Payments

Suppose you were to borrow $100,000 at 6% for 30 years, to be repaid monthly. To calculate the monthly payment, convert percentages to decimal format, then follow the formula:

  • a: $100,000, the amount of the loan
  • r: 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)
  • n: 360 (12 monthly payments per year times 30 years)

Here's how the math works out:

100,000 ÷ { [ ( 1 + 0.005 ) 360 ] - 1 } ÷ [ 0.005 ( 1 + 0.005 ) 360 ] = 599.55

The monthly payment is $599.55. If you're unsure, you can check your math with an online loan calculator.

Interest-Only Loan Payments

Using the previous loan example of $100,000 at 6%, your calculation would look like this:

  • a: $100,000, the amount of the loan
  • r: 0.06 (6% expressed as 0.06)
  • n: 12 (based on monthly payments)

Here's the math:

Using the second method, it would look like this:

 ( 100,000 * 0.06 ) / 12 = 500

You can check your math with an interest-only calculator if you're not sure you did it right.

Credit Card Payments

If you owe $7,000 on your credit card, and your minimum payment is calculated as 1% of your balance, here's how it would look:

$7,000 * 0.01 = $70

This amount does not include any late fees or other penalties you might owe. If you're uncertain, you can check your math with a credit card payment calculator.

Because your credit card charges interest monthly, your balance changes every month. That affects how much your minimum monthly payment will be. In many cases, the minimum monthly payment on a high balance will not be enough to cover the accrued interest.

It’s good practice to pay more than the minimum due each month, but the minimum is the amount you must pay to avoid late charges and other penalties.

For example, if the card in the previous example with a $7,000 balance has a 19.99% annual percentage rate (APR), you would calculate your monthly interest charges using this formula, where (B) is monthly balance and (I) is your new monthly balance:

APR Formula

Here's how it works for your new credit card balance:

$7,000 ( 19.99% ÷ 12) = $,7000 ( .1999 ÷ 12) = $7,000 ( 0.0166 ) = $116.20

Then, add the interest to your balance and calculate your minimum payment:

$7,116.20 * .01 = $71.16

As you can see, the interest charges exceed the minimum monthly payment, so the balance would continue to grow even if you make the minimum payment each month.

What It Means for Consumers

Calculating your monthly payments can help you figure out whether you can afford to use a loan or credit card to finance a purchase. It helps to take the time to consider how the loan payments and interest add to your monthly bills. Once you calculate your payments, add them to your monthly expenses and see whether it reduces your ability to pay necessary and living expenses.

If you need the loan to finance a necessary item, prioritize your debts to try and pay the ones that cost you the most as early as possible. As long as there's no prepayment penalty, you can save money by paying extra each month or making large lump-sum payments.

It helps to talk to your lender before you begin making extra or lump-sum payments. Different lenders might increase or decrease your monthly payments if you change your payment amount. Knowing in advance can save you some headaches down the road.

Key Takeaways

  • By using loan payment calculations, you can figure out whether you can realistically afford to borrow money.
  • Factors such as your income and monthly expenses will aid you in deciding whether taking a loan is a good idea.
  • With interest-only loans and amortizing loans, you can solve for what your monthly payments would look like.
  • Paying off your loan as quickly as possible can minimize the amount of interest you'll pay on the borrowed money.

Frequently Asked Questions (FAQs)

What are semi-monthly payments?

Semi-monthly payments are those that occur twice per month.

How do you make monthly payments on Amazon?

If an item is eligible for monthly payments on Amazon, you simply need to select monthly payments at checkout. The payments will be automatically deducted from your account's primary credit card.

How do you make monthly payments to the IRS?

If you don't think you'll be able to file your taxes and pay your balance on time, you can request a payment plan with the Internal Revenue Service online.

Article Sources

  1. Consumer Financial Protection Bureau. "What Is an 'Interest-Only' Loan?" Accessed Nov. 19, 2021.

  2. Consumer Financial Protection Bureau. "What Is Amortization and How Could It Affect My Auto Loan?" Accessed Nov. 19, 2021.

  3. California State Board of Equalization. "Lesson 7: Periodic Repayment (Assessors’ Handbook 505, Column 6)." Accessed Nov. 19, 2021.

  4. MIT OpenCourseWare. "Chapter 17: Mortage Basics II: Payments, Yields, and Values." Accessed Nov. 19, 2021.

  5. Bank of America. "Example of Credit Card Agreement for Bank of America Visa Signature Accounts," Page 8. Accessed Nov. 19, 2021.

  6. Board of Governors of the Federal Reserve. "Regulation Z Truth in Lending: Introduction," Page 12-19. Accessed Nov. 19, 2021.

  7. Consumer Financial Protection Bureau. "Can I Prepay My Loan at Any Time Without Penalty?" Accessed Nov. 19, 2021.