To calculate a payment with interest, you need three pieces of information: the amount borrowed (principal), the interest rate, and the repayment period. The exact formula depends on whether you’re dealing with a simple one-time payment, a fixed monthly installment like a mortgage or car loan, or revolving credit like a credit card. Here’s how each calculation works, with examples you can follow step by step.
Simple Interest: The Starting Point
Simple interest is the most straightforward calculation. You multiply the principal by the interest rate by the time period:
Interest = Principal × Rate × Time
If you borrow $5,000 at 6% annual interest for 3 years, the total interest is $5,000 × 0.06 × 3 = $900. Your total repayment would be $5,900. Simple interest is commonly used for auto loans, student loans, and some mortgages. Banks also use it to calculate what they pay you on savings accounts.
The key feature of simple interest is that it’s calculated only on the original principal, not on accumulated interest. That makes it predictable and easy to estimate. But most consumer loans with monthly payments use a more complex formula, because you’re paying down the balance gradually over time.
Monthly Payments on Installment Loans
Mortgages, car loans, and personal loans typically require equal monthly payments that cover both principal and interest. Each payment chips away at the balance, which means the interest portion shrinks over time while the principal portion grows. This structure is called amortization.
The formula for calculating a fixed monthly payment is:
Monthly Payment = Loan Amount × [i × (1 + i)^n] / [(1 + i)^n − 1]
In this formula, “i” is your monthly interest rate (annual rate divided by 12) and “n” is the total number of payments (loan term in years multiplied by 12).
A Worked Example
Say you’re borrowing $25,000 for a car at 6% annual interest over 4 years. First, convert the rate and term:
- Monthly rate (i): 0.06 ÷ 12 = 0.005
- Number of payments (n): 4 × 12 = 48
Now plug those into the formula:
Payment = $25,000 × [0.005 × (1.005)^48] / [(1.005)^48 − 1]
First calculate (1.005)^48, which is approximately 1.2705. Then:
- Numerator: 0.005 × 1.2705 = 0.006353
- Denominator: 1.2705 − 1 = 0.2705
- Payment: $25,000 × (0.006353 ÷ 0.2705) = $25,000 × 0.02348 = $587.00
Your monthly payment would be about $587. Over 48 months, you’d pay a total of roughly $28,176, meaning about $3,176 goes to interest.
How Interest Shifts Within Each Payment
In month one, the interest portion of your $587 payment is $25,000 × 0.005 = $125. That leaves $462 going toward principal, reducing your balance to $24,538. In month two, interest drops slightly to $24,538 × 0.005 = $122.69, and more of your payment goes to principal. By the final months, almost the entire payment is principal. This gradual shift is why paying extra early in a loan saves the most interest over time.
Credit Card Interest Calculations
Credit cards work differently from installment loans. Instead of a fixed payment schedule, your interest compounds daily on whatever balance you carry. Most issuers use the average daily balance method.
Here’s how it works in practice. Your card issuer takes your APR and divides it by 365 to get a daily periodic rate. If your APR is 22%, your daily rate is about 0.0603%. Each day, that rate is applied to your current balance, and the resulting interest is added. At the end of your billing cycle, all that daily interest gets totaled into your statement.
Because interest accrues daily, carrying a $3,000 balance at 22% APR doesn’t simply cost $3,000 × 0.22 ÷ 12 = $55 per month. The actual charge will be slightly higher due to compounding, and it varies depending on when during the month you make payments or new purchases. The practical takeaway: paying down your balance sooner, even mid-cycle, reduces the interest you owe because it lowers your average daily balance.
If your card has a grace period (most do), you won’t owe any interest on new purchases as long as you pay your full statement balance by the due date. Interest only kicks in when you carry a balance from one cycle to the next.
Using a Spreadsheet to Calculate Payments
You don’t need to do this math by hand. Excel and Google Sheets both have a built-in PMT function that calculates fixed loan payments instantly. The syntax is:
=PMT(rate, nper, pv)
- rate: The interest rate per period. For monthly payments, divide the annual rate by 12.
- nper: The total number of payments. For a 4-year loan, enter 48.
- pv: The present value, meaning the loan amount.
Using the car loan example above, you’d type: =PMT(0.06/12, 48, 25000). The result will show as a negative number (around -$587) because it represents money going out. That’s normal.
The function also accepts two optional inputs. “fv” is the future value, or the balance you want remaining after the last payment (defaults to zero, which is what you want for a standard loan). “type” controls whether payments happen at the end of each period (enter 0 or leave blank) or the beginning (enter 1). For most loans, leave both optional fields empty.
The critical rule is keeping your units consistent. If you enter a monthly rate for “rate,” your “nper” must also be in months. Mixing an annual rate with monthly periods will give you a wildly wrong answer.
How Day-Count Conventions Affect Interest
One detail that can cause small discrepancies in your calculations: not all lenders count days the same way. Some use a 360-day year, dividing your annual rate by 360 instead of 365 to get a daily rate. This convention, common in money market products and some commercial loans, produces a slightly higher daily rate (and therefore slightly more interest) than dividing by 365.
For a $200,000 balance at 6%, the daily rate using a 360-day year is 0.01667%, while a 365-day year gives 0.01644%. Over a full year, that difference adds up to roughly $164 in extra interest. Consumer mortgages and auto loans typically use 365 days, but your loan documents will specify which method applies. If your own calculations are a few dollars off from your lender’s statement, the day-count convention is often the reason.
Estimating Total Interest Over the Life of a Loan
Once you know your monthly payment, finding total interest is simple arithmetic. Multiply the monthly payment by the number of payments, then subtract the original loan amount. Using the earlier example: $587 × 48 = $28,176 total paid, minus $25,000 borrowed, equals $3,176 in total interest.
This calculation is useful for comparing loan offers. A lender offering 5.5% over 48 months on that same $25,000 loan would give you a payment of about $581, with total interest around $2,876. The $6 per month difference saves $300 over the life of the loan. On larger loans like mortgages, even a quarter-point difference in rate can mean tens of thousands of dollars.
Extending the loan term lowers monthly payments but increases total interest dramatically. That same $25,000 at 6% stretched to 6 years (72 months) drops the payment to about $414, but total interest rises to roughly $4,800. You’d pay an extra $1,600 for the convenience of lower monthly payments.