Simple vs compound interest, and how interest becomes return

What is the difference between simple and compound interest?

Interest is the price of using money: a borrower pays it to a lender. The difference between the two kinds is what the interest is calculated on.

• Simple interest is calculated only on the original amount, called the principal. It adds the same dollars every year.
• Compound interest is calculated on the principal plus all the interest already added. Each year’s interest earns interest of its own, so the amount added grows every year.

Over a year or two the gap is small. Over decades it is enormous, and it works the same way whether you are the one earning the interest or the one paying it.

How does simple interest work?

Multiply the principal by the yearly rate and the number of years. The interest never changes, because the base never changes.

Where simple interest shows up

• Auto loans. The Consumer Financial Protection Bureau (CFPB) says simple interest is far more common on auto loans than precomputed interest. It is charged on the balance you still owe, so paying extra shrinks the principal and the interest that follows.
• Bonds that pay a fixed coupon. A bond’s interest is paid out to you rather than added to the balance. It only compounds if you reinvest it yourself.
• Some short-term loans, including informal ones between family or friends, where interest is figured as principal × rate × time.

The alternative the CFPB contrasts it with is precomputed interest: the total interest for the whole loan is worked out up front and folded into the payments. With precomputed interest, the CFPB notes, extra payments do not reduce the principal or the interest you owe. If you plan to pay a loan off early, it is worth confirming which kind you have before you sign.

How does compound interest work?

Interest is added to the balance at set times, and the next round of interest is figured on the new, larger balance. The general formula allows for any number of additions per year:

Both in a spreadsheet

Simple interest is plain multiplication: =5000*6%*4 returns 1,200. Compound interest uses FV, or the formula written out: =FV(6%, 4, 0, -5000) and =5000*(1+6%)^4 both return 6,312.38. (FV shows money you hand over as a negative number, which is why the −5000.)

Simple vs compound interest calculator

Enter an amount, a rate and a number of years to see both kinds side by side, year by year.

With the calculator’s starting numbers, $10,000 at 6% compounded yearly, the two pull apart like this:

Simple interest draws a straight line: $600 a year, forever. Compound interest draws a curve that bends upward, and after 40 years it has triple the money.

The higher the rate, the faster the two split. Here is $10,000 after 20 years:

What is the difference between APR and APY?

APR is the quoted yearly rate without compounding; APY is what you actually earn in a year once compounding is counted. The federal Truth in Savings rule (Regulation DD) defines APY as a rate reflecting the total interest paid, based on the interest rate and how often it compounds, over a 365-day period. It defines the plain interest rate as one that “does not reflect compounding.”

In Excel or Google Sheets, EFFECT converts APR to APY: =EFFECT(5%, 12) returns 0.051162, or 5.116%. NOMINAL goes the other way: =NOMINAL(5.12%, 12) returns 0.050036, the APR compounded monthly that gives a 5.12% APY.

The lesson: compare savings accounts by APY, and remember that a card or loan’s APR understates what unpaid interest really costs once it compounds.

When does compound interest work against you?

Whenever you owe money and unpaid interest gets added to the balance. Credit cards are the main example. The CFPB explains that many card companies calculate interest daily, using a daily periodic rate: the APR divided by 360 or 365, depending on the issuer. That day’s interest is added to the balance, so it compounds daily.

Real cards differ in their balance method, fees and minimum payments, so your statement will not match this exactly; your card agreement has the details. The direction is the same, though: interest you do not pay starts charging interest of its own.

How does interest relate to return?

Interest is one way money earns money. Return is the whole picture: everything your money earns from any source, as a share of what you put in. Interest from a savings account or bond is one source. Dividends from stocks, rent from property and a rise (or fall) in price are others.

$10,000 that is worth $11,200 a year later and paid $300 in dividends returned ($11,200 + $300 − $10,000) ÷ $10,000 = 15%.

Two differences matter:

• Interest is usually known in advance; returns are not. A 5% APY is 5% if rates hold. A stock fund’s return could be +25% or −30% in a given year.
• Returns compound too. Gains that stay invested earn gains of their own, which is why long-run returns are quoted as a compound yearly rate. The S&P 500 compounded about 10.0% a year from 1928 to 2025, while its simple average yearly return was 11.9%, with 26 losing years out of 98. The future can be worse, so for planning we use a cautious 7% a year before inflation.

Why the bridge matters

Putting everything in the same unit, a compound yearly rate, lets you compare choices that look unrelated. A savings account’s APY, a planning return on investments and a credit card’s effective rate are all answers to one question: what does a dollar here earn or cost per year?

Lined up that way, some decisions make themselves. A card charging an effective 27% a year costs far more than a 7% planning return could earn, so paying off the card comes first. A savings account at a known rate is the right home for money you will need soon, because a higher expected return always comes with a chance of losing money in any given year. The rate tells you the reward; the kind of return tells you the risk.

What do people get wrong about simple and compound interest?

• “Simple interest loans are cheap.” Simple interest only means interest is not charged on interest. A high-rate simple interest loan still costs a lot; the car loan above costs $4,701.80 at 7%.
• “Compounding frequency is what matters most.” Going from monthly to daily compounding on 5% adds about a hundredth of a percentage point. The rate and the years matter far more.
• “The APR on my card is what it costs.” Only if you never let interest sit on the balance. Unpaid interest compounds, so the true yearly cost runs above the APR.
• “An average return works like an interest rate.” A fixed rate compounds smoothly. Investment returns jump around, and the simple average of those returns overstates what the money actually grew at. The compound yearly rate is the honest one.
• “Simple interest is only a classroom idea.” The CFPB calls it the far more common method on auto loans, many bond coupons work that way, and it is the right way to figure a quick month of interest on any balance.

Which is better, simple or compound interest?

It depends which side of the money you are on.

• Saving or investing: compound is better. You want your interest to earn interest, as often as possible, for as long as possible.
• Borrowing: simple interest on a balance that shrinks is better. It lets every extra payment cut future interest, and unpaid interest does not grow on itself.

For short periods the difference is small. For anything measured in decades, retirement savings, a mortgage, a card balance you never quite clear, compounding is the force that decides the outcome. Put it on your side twice: let your savings compound for as long as possible, and never let a balance you owe sit long enough to compound against you.