To calculate interest on a loan, you need three numbers: the amount you borrowed (principal), the interest rate, and the length of the loan. The simplest version of this math is Principal × Rate × Time, but most real-world loans use a more complex method that recalculates interest each month based on your remaining balance. Here’s how both approaches work so you can figure out exactly what a loan will cost you.
Simple Interest: The Basic Formula
Simple interest is the most straightforward calculation. The formula is:
Interest = P × r × n
- P = Principal (the amount you borrow)
- r = Annual interest rate (as a decimal)
- n = Loan term in years
Say you borrow $10,000 at 6% interest for 3 years. Plug those numbers in: $10,000 × 0.06 × 3 = $1,800. You’d pay $1,800 in total interest over the life of the loan, making your total repayment $11,800.
Some personal loans, auto loans, and short-term loans use simple interest. The key feature is that interest is calculated only on the original amount you borrowed, not on any accumulated interest. That makes the math predictable, but it’s not how most large loans work.
How Amortized Loans Calculate Interest
Most mortgages, car loans, and student loans are amortized. That means you make equal monthly payments, but the split between interest and principal changes every month. Early in the loan, most of your payment goes toward interest. As your balance shrinks, more of each payment chips away at the principal.
Here’s how the monthly interest portion works. Take your annual interest rate, divide it by 12, and multiply by your current loan balance. For example, on a $30,000 loan at 3% interest, the first month’s interest charge is $30,000 × 0.03 ÷ 12 = $75. If your total monthly payment is $664, then $75 goes to interest and $589 goes toward reducing the balance. The next month, interest is calculated on the slightly lower balance of $29,411, so the interest portion drops and the principal portion grows.
To calculate the total monthly payment on an amortized loan, the formula 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 monthly payments. For a $200,000 mortgage at 7% over 30 years, i = 0.07 / 12 = 0.00583, and n = 360. Running that math gives you a monthly payment of about $1,331. Over 30 years, you’d pay roughly $279,000 in interest on top of the $200,000 you borrowed.
You don’t need to do this by hand. Online loan calculators handle the formula instantly. But understanding the mechanics helps you see why making extra payments early in a loan saves so much money: you’re reducing the balance that interest is calculated on for every remaining month.
Daily vs. Monthly Interest Accrual
Not all loans calculate interest on the same schedule. Some accrue interest monthly, while others accrue it daily. The difference matters more than you might expect.
With daily accrual, the lender divides your annual rate by 365 and charges that fraction of interest on your balance every day. On a $20,000 loan at 5%, daily interest is $20,000 × 0.05 / 365 = $2.74 per day. If interest compounds daily rather than monthly, the accumulated interest gets added to your balance sooner, which means tomorrow’s interest is calculated on a slightly higher number. Over years, daily compounding results in a higher total cost than monthly compounding at the same stated rate.
This is common with credit cards, some private student loans, and certain variable-rate products. The practical takeaway: if your loan accrues interest daily, paying even a few days earlier each month reduces total interest costs. Conversely, letting a balance sit untouched between payments costs you more than it would on a monthly-accrual loan.
Why APR Gives You the Real Cost
The interest rate on your loan agreement doesn’t always tell you the full cost of borrowing. Lenders often charge origination fees, closing costs, or other upfront charges that effectively raise what you’re paying. That’s where APR, or annual percentage rate, comes in. APR folds those fees into a single percentage that represents the true yearly cost of the loan.
For example, a mortgage might advertise a 6.5% interest rate, but after factoring in $4,000 in origination fees and $2,000 in other closing costs, the APR could be 6.75%. If you roll those fees into the loan balance instead of paying them upfront, your balance increases, and so does the APR.
When comparing two loan offers, APR is the better number to use. A loan with a lower interest rate but high fees can end up costing more than a loan with a slightly higher rate and no fees. Federal law requires lenders to disclose APR, so you’ll see it on every loan estimate or credit card offer.
Putting the Math to Work
Knowing how interest is calculated lets you make smarter borrowing decisions. Here are a few ways to use this knowledge:
- Compare loan terms: A 5-year auto loan at 6% on $25,000 costs about $3,999 in total interest. Stretch that to 7 years at the same rate and you’d pay about $5,663. The monthly payment drops, but you pay over $1,600 more.
- See the impact of extra payments: On an amortized loan, any extra money you pay goes directly to principal. That lowers the balance that next month’s interest is calculated on, creating a compounding savings effect over time.
- Evaluate refinancing: If you can lower your interest rate by even half a percentage point on a large balance, run the numbers. On a $200,000 mortgage, dropping from 7% to 6.5% saves roughly $80 per month and tens of thousands over the loan’s life.
For quick calculations, multiply your loan balance by your annual rate to get a rough annual interest cost, then divide by 12 for an approximate monthly figure. For precise amortization schedules showing the exact interest and principal breakdown of every payment, use a free online calculator where you can input your specific loan amount, rate, and term.