The most common formula for loan interest is Simple Interest = Principal × Rate × Time, but the formula you need depends on whether your loan charges simple interest or uses an amortization schedule with equal monthly payments. Most auto loans, personal loans, and mortgages use amortized payments, which require a different calculation. Here’s how both formulas work, with step-by-step examples you can follow with a calculator.
The Simple Interest Formula
Simple interest is the most straightforward way to calculate what you’ll owe on a loan. The formula is:
Interest = P × R × T
- P = Principal (the amount you borrowed)
- R = Annual interest rate (as a decimal)
- T = Time (in years)
Say you borrow $10,000 at 6% interest for 3 years. Convert 6% to a decimal (0.06), then multiply: $10,000 × 0.06 × 3 = $1,800 in total interest. Your total repayment would be $11,800. If you wanted to know how much interest accrues in just one month, you’d set T to 1/12: $10,000 × 0.06 × (1/12) = $50.
This formula works well for short-term loans and situations where you’re paying a lump sum at the end. Some auto loans, student loans, and short-term personal loans use simple interest. But most installment loans (where you make equal monthly payments over time) use the amortized payment formula below, even though the underlying interest charge on each payment is still based on simple interest math.
The Amortized Loan Payment Formula
When you take out a mortgage, car loan, or personal loan with fixed monthly payments, your lender uses an amortization formula to calculate what you pay each month. The formula looks intimidating, but each piece is simple once you break it down:
Monthly Payment = Loan Amount × [ i × (1 + i)^n ] / [ (1 + i)^n − 1 ]
- i = Monthly interest rate (your annual rate divided by 12)
- n = Total number of monthly payments
Let’s walk through an example. You borrow $20,000 for a car at 5.4% annual interest for 5 years.
First, find your monthly rate: 0.054 / 12 = 0.0045. Next, find total payments: 5 years × 12 months = 60. Now plug those into the formula:
Monthly Payment = $20,000 × [ 0.0045 × (1.0045)^60 ] / [ (1.0045)^60 − 1 ]
Calculate (1.0045)^60 = approximately 1.3093. So the numerator becomes 0.0045 × 1.3093 = 0.005892, and the denominator becomes 1.3093 − 1 = 0.3093. Divide: 0.005892 / 0.3093 = 0.019047. Multiply by $20,000 and your monthly payment is about $380.94.
Over 60 payments, you’d pay $22,856 total, meaning $2,856 goes to interest. That’s more than the simple interest formula would suggest ($20,000 × 0.054 × 5 = $5,400) because with amortization, you’re paying down the principal gradually, so each month’s interest charge shrinks. The amortized structure actually saves you money compared to paying simple interest on the full balance for the entire term.
How Each Monthly Payment Splits Between Interest and Principal
With an amortized loan, each monthly payment covers two things: interest on your current remaining balance, and a chunk that reduces the principal. Early in the loan, most of your payment goes to interest. By the end, almost all of it goes to principal. Here’s how to calculate the split for any single payment.
Take the same $20,000 car loan at 5.4% with a $380.94 monthly payment. For your first payment, multiply the remaining balance by the monthly rate: $20,000 × 0.0045 = $90 in interest. The rest of the payment, $380.94 − $90 = $290.94, reduces your principal. Your new balance is $19,709.06.
For the second payment, interest is calculated on that lower balance: $19,709.06 × 0.0045 = $88.69. Now $292.25 goes to principal. Each month the interest portion drops and the principal portion grows. By payment 60, you’d owe almost nothing in interest and nearly the entire $380.94 would knock out the remaining balance.
You can build a full amortization schedule in a spreadsheet by repeating this calculation for every payment. Column A is the payment number, column B is the interest charge (remaining balance × monthly rate), column C is the principal portion (monthly payment minus interest), and column D is the new remaining balance.
How Daily Interest Accrual Works
Credit cards and some variable-rate loans don’t calculate interest monthly. Instead, they use a daily periodic rate, which is your APR divided by the number of days in the year (either 365 or 360, depending on the lender).
If your credit card APR is 22%, your daily rate is 0.22 / 365 = 0.000603, or about 0.06% per day. On a $3,000 balance, one day of interest costs $3,000 × 0.000603 = $1.81. Over a 30-day billing cycle, that’s roughly $54.25.
The distinction between a 360-day and 365-day year matters more than it sounds. Dividing by 360 produces a slightly higher daily rate, which means you pay a little more interest over time. The 360-day convention is common for commercial and money market loans. Consumer credit cards and most personal loans typically divide by 365.
Converting Between Annual, Monthly, and Daily Rates
Every loan interest calculation starts with converting the annual rate to match the period you’re calculating. Here’s the quick reference:
- Annual to monthly: Divide the annual rate by 12. A 7.2% annual rate becomes 0.6% per month (0.072 / 12 = 0.006).
- Annual to daily: Divide by 365 (or 360 for some commercial loans). A 7.2% annual rate becomes roughly 0.0197% per day.
- Monthly to annual: Multiply by 12. A 0.5% monthly rate equals 6% annually.
One subtlety: these conversions give you the nominal rate, not the effective annual rate. If interest compounds monthly, you actually pay slightly more per year than the stated annual rate. For a 12% nominal rate compounded monthly, the effective annual rate is about 12.68%. For most loan payment calculations, though, the nominal monthly rate is what goes into the formula.
Putting the Formulas to Work
Knowing these formulas lets you answer practical questions before you sign for a loan. Want to compare a 4-year loan versus a 5-year loan? Run the amortized payment formula for both terms and add up the total interest (monthly payment × number of payments, minus the loan amount). Curious how much an extra $100 per month saves you? Build a quick amortization schedule and watch how the payoff date moves forward.
For a fast sanity check on any installment loan, the simple interest formula gives you the maximum interest you’d ever pay (if you made no payments until the end). The amortized formula gives you the real number, which is always lower because you’re steadily reducing the balance. If a lender quotes you total interest that exceeds the simple interest calculation, something is off and you should look more closely at the terms.