Interest is calculated three different ways depending on the financial product, and the difference between them can be hundreds or thousands of dollars over time. Simple interest is what your auto loan uses. Compound interest is what makes a savings account grow and a credit card balance explode. Credit card interest is calculated using a daily periodic rate that is technically a third method. This guide walks through each formula with a worked example and shows you how to set up the calculation yourself — no calculator required.
Simple interest: the easiest formula
The simple interest formula is the one most people learn first.
Interest = Principal × Rate × Time
Where:
- Principal is the amount of the loan or deposit (in dollars).
- Rate is the annual interest rate, written as a decimal (5% = 0.05).
- Time is the term in years.
Worked example. A $10,000 personal loan at 6% simple interest for 3 years generates 10000 × 0.06 × 3 = $1,800 of interest. The total repaid is $11,800.
Simple interest is used on most auto loans, short-term personal loans, and some credit-builder loans. It is the cheapest way for a borrower because interest does not earn interest — each year's interest is calculated only on the original principal.
Compound interest: the savings formula
Compound interest is calculated on the principal plus all previously accumulated interest. The formula is:
A = P × (1 + r/n)^(n×t)
Where:
- A is the final amount.
- P is the principal.
- r is the annual rate (decimal).
- n is the number of compounding periods per year.
- t is the number of years.
Worked example. $10,000 deposited at 4% compounded monthly (n=12) for 3 years grows to 10000 × (1 + 0.04/12)^(12×3) = $11,272. The interest earned is $1,272.
Compare to simple interest at the same rate: 10000 × 0.04 × 3 = $1,200. The compounding adds $72 over three years — a small difference at low rates and short terms, but compounding's edge grows dramatically over decades and at higher rates.
Compound interest is used on savings accounts, certificates of deposit, money market accounts, and (effectively) credit card balances if you carry them.
Credit card interest: the daily periodic rate
Credit card interest is technically a flavor of compound interest, but it has its own rhythm. Issuers calculate interest each day on your average daily balance using a daily periodic rate equal to APR ÷ 365.
The steps:
- Convert APR to a daily rate:
daily_rate = APR / 365. A 24.99% APR card has a daily rate of0.2499 / 365 = 0.0006847. - Calculate the average daily balance for the billing cycle. This is the sum of each day's ending balance divided by the number of days in the cycle.
- Multiply:
interest = average_daily_balance × daily_rate × days_in_cycle.
Worked example. A $3,000 average daily balance at 24.99% APR over a 30-day cycle generates 3000 × 0.0006847 × 30 = $61.62 in interest charges that month. That interest gets added to next cycle's balance, which is what makes carrying a credit card balance so destructive over time.
How compounding frequency affects the math
The more often interest compounds, the higher the effective yield (or cost). At 5% nominal annual interest:
- Annual compounding: APY = 5.000%
- Semi-annual compounding: APY = 5.063%
- Quarterly compounding: APY = 5.095%
- Monthly compounding: APY = 5.116%
- Daily compounding: APY = 5.127%
The gap between annual and daily compounding at 5% is only about 13 basis points — small in any one year but meaningful on a $50,000 balance over a decade. This is why APY (annual percentage yield) is the right comparison metric for savings products: it bakes the compounding frequency into the headline rate.
Where to skip the math: use a calculator
For most consumer financial decisions, you do not need to do the calculation by hand. Free calculators from the CFPB, Bankrate, NerdWallet, and most major banks handle simple, compound, and credit card interest with the same inputs. The value of doing the math yourself once is understanding what the calculator is doing — so when the inputs feel off, you know to question them.
For people working to pay off a credit card balance, modeling the scenario in a calculator first — then setting up an aggressive autopay — cuts both interest and time substantially. And if you are also building credit, products like the Self Visa® Credit Card use a savings-backed model that operates on the inverse logic: the structure rewards on-time monthly payments with both savings and credit history, instead of charging revolving APR.
Frequently Asked Questions
How do you calculate simple interest on a loan?
Multiply the principal by the annual rate (as a decimal) by the term in years. A $5,000 loan at 7% for 4 years generates 5000 × 0.07 × 4 = $1,400 in simple interest. Total repaid is $6,400. Most U.S. auto loans and some personal loans use this formula.
What is the formula for compound interest?
A = P × (1 + r/n)^(n×t), where A is the future amount, P is the principal, r is the annual rate (decimal), n is the compounding periods per year, and t is the number of years. The formula reduces to simple interest if n=1 and t=1.
How is credit card interest calculated daily?
Credit card issuers convert your APR to a daily rate (APR ÷ 365), calculate your average daily balance for the cycle, and multiply: interest = avg_daily_balance × daily_rate × days_in_cycle. The interest added to the cycle becomes part of next cycle's balance, which is why credit card debt grows so quickly if not paid in full.
What is the difference between APR and interest rate?
The nominal interest rate is the bare percentage charged before compounding. APR (annual percentage rate) is the annual cost of a loan including the interest rate plus any fees, expressed as a yearly figure. APR is what borrowers should compare; the bare interest rate is just one input.
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