What your interest result shows
The headline is the interest for the method you chose. Beside it sits the same money under the other method, because the gap between simple and compound interest is what most people are actually trying to find out — and over long periods it is large.
The per-day figure is the practical one. It tells you what an extra day of an overdue balance costs, what paying a loan off mid-month saves, and whether a few days either side of a deadline matter. Interest is almost always accrued daily even when it is charged monthly, which is why a payoff quote changes depending on the date you request it for.
Simple and compound interest
Simple: I = P × r × t
Simple interest is charged only on the original amount, so it grows in a straight line — the same dollars every year, indefinitely. It is the exception rather than the rule: you meet it in court judgments, in some bonds and treasury instruments, in car loans structured on a simple-interest basis, and in many late-payment and prompt-payment terms.
Compound: I = P × ((1 + r/n)nt − 1)
Compound interest is charged on the balance including interest already added, so each period is calculated on a slightly larger number and the total accelerates. Savings accounts, credit cards, mortgages and student loans all work this way. The compound interest calculator goes further into what that does over decades, and the APY calculator converts a rate and a frequency into a figure you can compare between accounts.
Over one year at a modest rate the two are close. Over ten they are not, and the difference widens with the rate — which is why compounding is described as working for you in savings and against you in debt.
When the per-day figure matters
- Paying off a loan. A payoff quote is good only to a stated date, because interest accrues daily until the money arrives. Ask for the per-day figure and the quote makes sense.
- Overdue invoices. Late-payment terms are commonly a rate applied per day on the outstanding amount, which is what the federal prompt-payment rules use.
- Credit cards. Interest is usually calculated on an average daily balance, so paying a few days earlier genuinely reduces the charge — see the card payoff calculator for what that is worth over a full balance.
- Savings. Most accounts accrue daily and pay monthly, so the day you deposit affects that month’s interest.
What this calculator assumes
- A fixed rate for the whole period, and no payments in or out — this measures interest on a static balance.
- 365-day years for the daily figures. Some contracts use 360, which raises the daily amount slightly; the paperwork will say which.
- No fees or tax. Interest earned is usually taxable in the year it is credited.
- No repayments. For a loan being paid down, the balance falls each month and so does the interest — use the amortization calculator for that.
These are planning estimates. Your agreement is the authority on the rate, the compounding frequency and the day-count convention.
Interest questions people ask
Is my loan simple or compound interest?
Most consumer loans compound, though many are described as "simple interest" because interest is calculated on the outstanding principal rather than on accrued interest. The practical test is whether unpaid interest is ever added to the balance: if it is, it compounds. Your agreement will state the method and the frequency.
Why does my payoff quote change if I pay a few days later?
Because interest accrues daily. A quote is calculated to a specific date, and every day past it adds the per-day amount shown above. On large balances that can be a meaningful sum over a week.
What is the difference between interest rate and APY?
The interest rate is the headline figure; APY is what that rate is worth after a year of compounding. APY is therefore equal to or higher than the rate, and it is the only figure that lets you compare two accounts with different compounding frequencies.
Does the day-count convention really matter?
On short periods and large balances, yes. A 360-day year makes each day slightly more expensive than a 365-day year at the same stated rate, which is why commercial agreements specify the convention explicitly.