How to Calculate Principal and Interest on a Loan

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To calculate principal and interest on a loan payment, multiply the current loan balance by the annual interest rate and divide by 12. That gives the interest portion of this month’s payment. Subtract it from your total payment, and the remainder is the monthly principal portion, the amount that reduces what you owe. Repeat the calculation each month on the new, lower balance. On a fixed-rate amortizing loan the payment stays the same. Each month, slightly less of it goes to interest and slightly more goes to principal.

Key takeaways

• Principal is the amount you borrowed and still owe. Interest is what the lender charges for letting you use that money.
• Monthly interest = current balance × (annual rate ÷ 12). Monthly principal = payment − monthly interest.
• The standard loan payment formula sets a fixed payment that pays the loan off exactly by the end of the term.
• The simple interest formula (P × R × T) gives total interest only when the full principal stays outstanding for the whole period.
• Your payment is calculated from the interest rate. The APR adds fees and is a tool for comparing offers.

Principal vs. Interest

Principal is the original amount you borrow, excluding interest. If you buy a $355,000 home with a $55,000 down payment, you borrow $300,000. That $300,000 is the principal. As you make payments, the outstanding principal (your loan balance) shrinks.

Interest is the price of borrowing. Lenders express it as an annual percentage of the outstanding balance. On an installment loan such as a mortgage, auto loan or personal loan, interest is usually charged only on the principal you still owe. That is why the interest cost falls as the balance falls.

A single payment therefore has two jobs. The interest portion pays for the past month of borrowing and does not reduce your debt. The principal portion repays the loan itself.

How to Calculate the Monthly Principal and Interest Split

The method below applies to a standard fixed-rate loan with monthly payments.

1. Find the monthly rate. Divide the annual interest rate by 12. A 4% annual rate is 0.04 ÷ 12 = 0.003333 per month.
2. Calculate the interest portion. Multiply the current balance by the monthly rate.
3. Calculate the principal portion. Subtract the interest portion from your scheduled payment.
4. Update the balance. Subtract the principal portion from the balance. The result is the starting balance for next month.

Worked Example: $300,000 Mortgage at 4% for 30 Years

Hypothetical example for illustration. Assumptions: fixed 4% rate, 360 monthly payments, no extra payments, and figures for principal and interest only.

The scheduled payment on this loan is $1,432.25 (the formula is in the next section).

• Month 1 interest: $300,000 × 0.04 ÷ 12 = $1,000.00
• Month 1 principal: $1,432.25 − $1,000.00 = $432.25
• New balance: $300,000 − $432.25 = $299,567.75
• Month 2 interest: $299,567.75 × 0.04 ÷ 12 = $998.56
• Month 2 principal: $1,432.25 − $998.56 = $433.69

The interest portion drops by about $1.44 in the second month, and the principal portion rises by the same amount. Over the life of the loan, the split moves like this:

Halfway through the term, about $193,600 of the original $300,000 is still owed. That is why early payments feel slow: the balance is large, so interest takes most of each payment. Over 30 years the borrower pays $1,432.25 × 360 = $515,610 in total. That is $300,000 of principal and $215,610 of interest.

A month-by-month table of these figures is called an amortization schedule. Our guide to the amortization schedule shows how to build one in full.

The Loan Payment Formula

Lenders set the fixed payment on an amortizing loan with this formula:

M = P × [r(1 + r)^n] ÷ [(1 + r)^n − 1]

• M = monthly payment (principal and interest)
• P = principal borrowed
• r = monthly interest rate (annual rate ÷ 12, as a decimal)
• n = total number of monthly payments

For the example: r = 0.003333 and n = 360. (1.003333)^360 is about 3.3135, so M = 300,000 × (0.003333 × 3.3135) ÷ 2.3135, or about $1,432.25.

Principal Portion of Any Payment

You don’t need to step through every month to find the principal in a given payment. On a fixed-rate loan with no extra payments, the principal portion grows by a factor of (1 + r) each month:

Principal in payment k = (M − P × r) × (1 + r)^(k − 1)

M − P × r is the first month’s principal ($432.25 in the example). For payment 181: $432.25 × (1.003333)^180 = $432.25 × 1.8203, or about $786.83. This matches the table. The interest portion is then M minus that figure.

Remaining Balance After k Payments

Balance = P(1 + r)^k − M × [(1 + r)^k − 1] ÷ r

After 180 payments: $300,000 × 1.8203 − $1,432.25 × (0.8203 ÷ 0.003333) is about $546,090 − $352,464, or roughly $193,627. Multiply that balance by r and you get the next month’s interest.

Simple Interest: P × R × T

The basic principal interest formula is:

Simple interest = P × R × T

• P = principal
• R = annual interest rate (decimal)
• T = time in years

Hypothetical example: $10,000 at 6% for 3 years gives $10,000 × 0.06 × 3 = $1,800 of interest.

That result holds only if the full $10,000 is outstanding for all three years, as with an interest-only loan or a single repayment at the end. On a loan you repay monthly, the balance falls with each payment, so total interest comes out lower than P × R × T. “Simple interest” in consumer lending usually means interest accrues on the outstanding principal only, not on unpaid interest. Credit cards are different: unpaid interest can be added to the balance and then charged interest itself, which is compounding.

Daily Interest Accrual

Some loans, including many auto loans, accrue interest daily instead of calculating it once a month:

Interest = balance × (annual rate ÷ 365) × days since last payment

On these loans, timing matters. Paying a few days early means fewer days of interest, so a little more of the payment goes to principal. Paying late shifts more of the payment to interest. Some lenders use a 360-day year in this formula, which slightly increases the daily charge.

Working Backward From What You Know

Rearranging the same relationships answers common questions.

Principal from monthly interest. Principal = monthly interest × 12 ÷ annual rate. Example: if $235 of monthly interest is charged at 3%, the balance is $235 × 12 ÷ 0.03 = $94,000.

Interest from a mortgage payment. With only the payment and rate, you still need the current balance. Interest = balance × rate ÷ 12. For instance, $300,000 × 6.625% ÷ 12 = $1,656.25 of interest for that month.

Rate from principal and total simple interest. R = I ÷ (P × T). Example: $1,800 of interest on $10,000 over 3 years gives 1,800 ÷ 30,000 = 6%. For an amortizing loan, solving for the rate from the payment has no simple rearrangement. Calculators find it by trial and iteration.

Percentage change in a balance. Divide the change by the starting amount. A balance that rises from $1,100.79 to $1,103.02 grew by $2.23, which is $2.23 ÷ $1,100.79, or about 0.20% for that period.

Interest still ahead of you. Total remaining interest = (monthly payment × remaining months) − current principal balance. In the example at the start of year 16: $1,432.25 × 180 − $193,627, or about $64,178. If you paid off the loan at that point with no prepayment penalty, that is roughly the scheduled interest you would avoid.

What Changes the Principal and Interest Split

Extra principal payments. An extra payment applied to principal lowers the balance immediately, so every later interest calculation starts from a smaller number. On a fixed-rate mortgage, the required payment usually stays the same and the loan ends sooner. Confirm that the lender applies the extra amount to principal and not to the next scheduled payment.

Adjustable-rate mortgages. An ARM has a fixed rate for an initial period, commonly 3, 5, 7 or 10 years (some FHA ARMs start with 1 year), then resets at set intervals based on market rates. At each reset, the remaining principal is multiplied by a new rate and the payment is recalculated over the remaining term. Your payment and its split can then rise or fall. Many ARMs start with a lower rate than comparable fixed-rate loans, which makes early payments cheaper but less predictable later.

Escrow and other costs. A monthly mortgage bill often includes property taxes, homeowners insurance and private mortgage insurance held in escrow. These raise what you pay each month. They do not change the principal and interest calculation or the balance you owe. In the example, $1,432.25 is principal and interest only.

Loans that don’t fully amortize. Interest-only loans and balloon loans do not follow the schedule above. During an interest-only period, the payment equals balance × rate ÷ 12 and the principal does not fall.

Interest Rate vs. APR

The interest rate is the percentage the lender charges on your balance, and it drives the monthly calculation. The annual percentage rate (APR) folds in costs such as origination fees, discount points, mortgage insurance and some closing costs. It is usually higher than the interest rate.

Use the interest rate to calculate your payment. Use the APR to compare offers: a loan with a low rate can carry a higher APR if its fees are heavy. Under the Truth in Lending Act’s Regulation Z, U.S. lenders must disclose the APR, and mortgage lenders show it on the Loan Estimate you receive after applying. For a fuller comparison, see interest rate vs. APR.

FAQs

The Bottom Line

Anyone paying a mortgage, auto loan or personal loan can check where each payment goes with a simple balance times monthly rate calculation. Early payments go mostly to interest, so extra payments applied to principal cut later interest charges and shorten the loan. Use the interest rate to figure your payment, and use the APR to compare offers, since fees can make a low-rate loan cost more.