What this comparison actually shows
Put the same principal, the same annual rate and the same length of time into two different rules and you get two different answers. Simple interest pays out the same amount every single period, calculated on the original principal alone. Compound interest folds each period's interest back into the balance, so the next period earns interest on a slightly bigger figure than the one before. On the calculator's own defaults, $10,000 at 5% over 10 years finishes at $15,000 under simple interest and $16,470 under monthly compounding, a $1,470 gap that exists purely because compounding lets interest earn its own interest along the way. Nothing here asks which formula matches your situation; it runs both, side by side, from the same three numbers, so the size of that gap is always in front of you rather than something you have to work out separately.
The two formulas, side by side
Simple interest is one line:
Compound interest adds a compounding frequency, n, the number of times a year interest is credited:
Both start from the same P, r and t; compound interest just applies its own result back to itself every 1÷n of a year instead of waiting until the end. A regular addition complicates the arithmetic for either formula, since a fresh contribution needs its own share of whatever time is left, so this calculator steps forward one month at a time for both methods rather than trying to force a running series of deposits through a single line of algebra. If you only care about one of the two formulas and want its full working shown step by step, the simple interest calculator solves I = Prt (and its three rearrangements) on its own, and the compound interest calculator goes deep on the compounding side, including what a bigger starting amount does versus a bigger monthly contribution.
Where simple interest actually turns up
Most consumer borrowing and saving compounds by default, which makes simple interest the exception rather than the rule. It still shows up in specific corners: car finance is commonly calculated on simple interest applied daily to whatever principal is still outstanding, so paying a bit early genuinely reduces the interest charged rather than just moving a fixed schedule forward. Short-dated government debt behaves the same way; a Treasury bill is typically sold at a discount and repaid at face value, which is functionally a single simple-interest payment rather than a compounding one, and many ordinary bonds pay a flat coupon that never reinvests automatically either. It is also, for what it is worth, the version taught first in almost every maths and business course, which is usually the reason the term "simple interest" gets searched for at all.
Where compound interest actually turns up
Compound interest is the default almost everywhere else money sits for more than a single period. Everyday savings accounts, cash ISAs and most fixed-term deposits credit interest back into the balance on a schedule, monthly or daily being typical, so the account genuinely earns interest on its own past interest. Credit cards work the same way in reverse: carry a balance past the due date and interest is charged on the outstanding amount, which then itself attracts interest the following month if it still is not cleared, the exact mechanism that makes revolving card debt so much more expensive to leave running than a fixed-term loan of the same headline rate. Investment accounts and pensions are usually modelled the same way for planning purposes, even though real returns bounce around year to year rather than compounding smoothly.
Does the compounding frequency actually matter?
Less than the dropdown suggests. Take a nominal 5% rate: compounded once a year it is exactly 5% by the end of the year; compounded daily it works out to 5.1267%, a difference of about 0.13 percentage points. That gap barely moves whether the account compounds monthly or daily; almost the whole effect comes from moving away from annual compounding at all, and after that the remaining choices are close together. The table above runs your own principal, rate, term and addition through annually, monthly and daily compounding so you can see the actual pound-or-dollar difference rather than a general rule, and in most everyday cases it is small next to what the rate itself or an extra year of saving would do.
The related figure lenders and savings providers actually publish is APR for borrowing and APY for saving, and they are not the same number even from the same nominal rate: APY folds in the compounding effect just described, so it is always a little higher than the nominal rate it is built from. The interest rate calculator converts between a nominal rate and its APY at any compounding frequency, and separately works out the real APR hiding inside a loan quote's amount, payment and term.
Two ways to ask when it doubles
Simple interest doubles a balance in exactly one divided by the rate, no estimating required, because I = Prt reaches P (doubling the total to 2P) precisely when r × t = 1. At 5% that is 1 ÷ 0.05 = 20 years, on the nose, every time. Compound interest gets there sooner and has no equally tidy formula, so two shortcuts exist instead: the rule of 72, which divides 72 by the rate for a fast mental estimate, and the exact figure, the natural log of 2 divided by the natural log of 1 plus the rate. At 5% the rule of 72 gives 72 ÷ 5 = 14.4 years against an exact 14.21 years, a few weeks apart; the rule stays close across the range most people use it for and drifts further only at unusually high rates. Neither figure accounts for a regular addition, which pulls the doubling date in far sooner than rate alone ever could.
The same maths, read as a debt instead of a gain
Every formula above cares only about a principal, a rate and a time; it has no idea whether that principal is money you put in or money you owe. The "reading this as" toggle exists purely to say the second half of that sentence out loud: switch it to borrowing and the identical numbers get described as interest owed rather than interest earned, the headline reads as a cost rather than a gain, and the chart's legend follows suit. Nothing about the arithmetic changes, which is exactly the point; a credit card balance compounds by the same rule a savings account does, and a car loan's daily simple interest is calculated the same way a short-term bond's coupon is, just pointed in the other direction.
Questions people ask
What's the real difference between simple and compound interest, in money terms?
On this calculator's own defaults, $10,000 at 5% over 10 years reaches $15,000 under simple interest and $16,470 under monthly compounding, a $1,470 gap. That gap is zero at the very start, grows slowly at first, and widens every year afterwards, which is exactly what the two-line chart above is built to show using your own figures rather than a fixed example.
Where does simple interest actually get used today?
Car finance is commonly calculated on simple interest applied daily to the remaining principal, short-dated government debt such as Treasury bills is effectively a single simple-interest payment sold at a discount, and many bonds pay a flat coupon rather than reinvesting it. It is also the version taught first in most maths and finance courses.
Where does compound interest actually get used today?
Everyday savings accounts, cash ISAs and fixed-term deposits credit interest back into the balance on a schedule, and credit cards charge compounding interest on any balance carried past the due date, which is why revolving card debt grows faster than a fixed loan at the same headline rate.
Does switching the compounding frequency actually change my result much?
A little, but far less than moving the rate itself. A nominal 5% rate compounded annually is exactly 5% by year end; compounded daily it comes to 5.1267%, a gap of about 0.13 percentage points. Monthly sits close to daily. The table above runs your own numbers through all three so you can see the actual amount rather than a general rule.
How accurate is the rule of 72 for finding doubling time?
Close, across the range most people use it for. At 5% it estimates 14.4 years against an exact 14.21, a few weeks out. It drifts further at unusually high rates, so treat it as a quick mental check and let the exact figure, or the calculator's own doubling-time block, carry the actual answer.
What's the difference between APR and APY?
APR is the rate lenders quote on borrowing; APY (sometimes called the effective annual rate) is what savers are quoted, and it is always a little higher than the nominal rate it is built from because it folds in the effect of compounding. The interest rate calculator converts between the two at any compounding frequency, and can also work out the real APR hiding inside a loan's amount, payment and term.
Does this calculator work if I'm calculating interest I owe, not interest I earn?
Yes. Switch the "reading this as" toggle to borrowing and the same formulas run on the same numbers; only the words change, from interest earned to interest owed. The maths behind a savings account and a debt is identical, which is the reason the toggle exists rather than a second calculator.
This calculator is for illustration and comparison. It is not financial advice, and real loans, savings products and investments may use different day-count conventions, fees or compounding terms; check the specific agreement before relying on any figure here.