What is the difference between simple and compound interest?

Simple interest pays only on the original principal — same dollar amount every period. Compound interest pays on principal plus all the interest accumulated so far, so each period's interest is slightly bigger than the last. On $10,000 at 6% for 20 years, simple interest gives you $22,000 total; compound interest (annually) gives you $32,071. The $10,071 gap IS compound interest.

What is the formula for simple interest?

I = P × r × t, where I is interest earned (or owed), P is the principal, r is the annual rate as a decimal, and t is time in years. To get the total amount including principal, use A = P × (1 + r × t). Example: $10,000 at 6% for 20 years gives I = 10,000 × 0.06 × 20 = $12,000 in interest, $22,000 total.

What is the formula for compound interest?

A = P × (1 + r/n)^(n·t). P is principal, r is the annual rate as a decimal, n is the number of compounding periods per year (1 for annual, 12 for monthly, 365 for daily), and t is time in years. Example: $10,000 at 6% compounded annually for 20 years gives A = 10,000 × (1.06)^20 ≈ $32,071.

Where do you actually see simple interest in real life?

Less often than you'd think. Most short-term US Treasury bills, some auto loans, certain personal loans, and bonds quoted at face are calculated with simple interest. Most other consumer products — savings accounts, credit cards, mortgages, investments — use compound interest in some form, usually with monthly or daily compounding.

Do credit cards really compound daily?

Yes, almost all of them. The card's APR is divided by 365 to get a daily periodic rate, which is applied to your average daily balance. A 24% APR card actually costs about 27.11% APY when compounded daily. On a $5,000 revolving balance, that's $1,355 in interest per year instead of the $1,200 the sticker rate suggests. The extra $155 is interest charging interest on itself every single night.

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Simple vs Compound Interest: How to Calculate Both

Drop $10,000 into an account at 6% for 20 years. With simple interest, you walk out with $22,000. With compound interest (annual), you walk out with $32,071. That $10,071 gap — earned without adding a single extra dollar — is compound interest. Here's how to calculate both, why the gap exists, and the places lenders quietly tilt the math against you.

Last updated: May 13, 2026.

The one-sentence distinction

Simple interest pays you (or charges you) only on the original principal. Compound interest pays on the principal plus every dollar of interest already earned. That's the whole difference, and over a long horizon it's the difference between a sedan and a Tesla.

Simple interest: the formula and a real example

The formula is the easiest one in personal finance:

I = P × r × t

I — interest earned or owed (a dollar amount).
P — principal (what you put in or borrowed on day one).
r — annual interest rate as a decimal. 6% is 0.06, not 6.
t — time in years.

To get the total amount including principal, just add P back:

A = P × (1 + r × t)

Worked example. $10,000 at 6% simple interest for 20 years:

I = 10,000 × 0.06 × 20 = $12,000

A = 10,000 + 12,000 = $22,000

Notice what's happening here: every single year, the interest earned is exactly $600 ($10,000 × 0.06). Year 1, year 5, year 20 — same flat $600. The interest never compounds onto itself. It just stacks like coins.

Compound interest: the formula and the same example

Compound interest takes one extra idea: at the end of each compounding period, the interest earned gets added to the principal, and the next period's interest is calculated on that new, larger balance.

A = P × (1 + r/n)^n·t

A — final amount.
P — starting principal.
r — annual rate as a decimal.
n — compounding periods per year (annual = 1, monthly = 12, daily = 365).
t — time in years.

Same $10,000 at 6%, compounded annually for 20 years:

A = 10,000 × (1 + 0.06/1)^1×20 = 10,000 × (1.06)²⁰ ≈ $32,071

Bump to monthly compounding (n = 12) and you get $33,102. Daily (n = 365) gives $33,198. The compounding frequency matters less than you'd guess — but the fact that interest compounds at all matters enormously.

The "aha" — year by year

The two formulas hide the magic. The table makes it obvious. Same $10,000, same 6%, simple vs compound (annual):

Year 1: Simple $10,600 · Compound $10,600 — identical.
Year 5: Simple $13,000 · Compound $13,382 — gap: $382.
Year 10: Simple $16,000 · Compound $17,908 — gap: $1,908.
Year 20: Simple $22,000 · Compound $32,071 — gap: $10,071.
Year 30: Simple $28,000 · Compound $57,435 — gap: $29,435.

Year 1, the two are identical. By year 5, compound is pulling ahead by a few hundred bucks. By year 20, compound has more than doubled the simple-interest result. By year 30, the gap is bigger than the original principal. Time is the lever. The longer you wait, the more violently the curves separate.

Where you see each one in the wild

Here's where the math actually shows up on real statements:

Simple interest territory:

US Treasury bills (T-bills) and most short-term Treasury notes — calculated on a simple-interest, day-count basis.
Some auto loans (especially "simple interest" auto financing — the marketing actually means it).
Certain personal loans from credit unions and federal student loans during in-school deferment.
Bonds purchased at face value with periodic coupon payments — each coupon is simple interest on the face amount.

Compound interest territory (almost everything else):

Savings accounts, money market accounts, CDs (typically daily or monthly compounding).
Credit cards (daily, on average daily balance).
Mortgages — technically simple interest in calculation, but practically compound: unpaid interest gets capitalized, and the amortization schedule front-loads interest in a way that behaves like compounding from the borrower's perspective.
Index funds, retirement accounts, and any reinvested-dividend strategy.
Most student loans after graduation, when accrued unpaid interest capitalizes onto the principal.

Rule of thumb: if it's marketed to you as a way to save or invest, it almost certainly compounds. If it's a short-term debt instrument issued by the government, it probably doesn't.

The trick lenders use

Here's the part the sticker rate doesn't tell you. Credit cards advertise an APR — say, 24%. They almost universally compound daily, not annually. The card divides 24% by 365 to get a daily periodic rate of 0.0658%, then applies that to your average daily balance every single night.

Run the numbers:

(1 + 0.24/365)³⁶⁵ − 1 ≈ 0.2711

That's a 27.11% effective annual rate, not 24%. On a $5,000 revolving balance held for a year, you pay $1,355 in interest, not the $1,200 the sticker rate implied. The extra $155 isn't a fee — it's interest charging interest on itself, every night, while you sleep.

Push the rate higher and the spread gets ugly fast. A 29.99% APR subprime card has a 34.96% APY when compounded daily. Nobody puts that number on the mailer because nobody would sign up.

Meanwhile, when banks pitch you a savings account, they advertise APY (the bigger compound number), not APR. Same math, opposite direction. Whoever is making money off the rate picks the flattering label. (Our APR vs APY article walks through that asymmetry in detail.)

Frequently asked questions

If compound interest is so much better, why does anyone offer simple interest?

Two reasons. First, regulation and convention — the Treasury market and parts of the bond market run on day-count simple interest because that's the long-standing standard, and it makes secondary trading cleaner. Second, marketing — "simple interest auto loan" sounds friendly because it means interest doesn't accrue on accrued interest if you make payments late. For the lender, simple interest is just easier to administer on short-duration debt.

Does compound interest always beat simple interest?

Over more than one compounding period at a positive rate, yes — always. They're identical at year zero and at the end of the first period. After that, compound pulls ahead and never looks back. The gap grows slowly at first, then violently. That's why people who start saving in their 20s end up with multiples of what people who start in their 40s end up with, even at the same monthly contribution.

Is mortgage interest simple or compound?

It's a hybrid that confuses everyone. The monthly interest is calculated as simple interest on the remaining balance — no compounding within the month. But because every payment changes the balance, and the schedule front-loads interest, the borrower experiences something that walks and quacks like compounding. If you ever miss a payment and the unpaid interest gets capitalized into the principal, that part is straight-up compound interest.

Which formula should I use for a quick mental estimate?

For short horizons (under 5 years) at moderate rates, simple interest gets you within a few percent of the right answer. For anything longer, use the Rule of 72: divide 72 by the rate to estimate when money doubles under compound interest. At 6% compounded annually, money doubles in about 12 years. Simple interest would take 16.7 years to double at the same rate. Big difference.

Can compound interest work against me?

Constantly. Any debt that compounds is the engine running in reverse. Carrying a $5,000 credit-card balance at 24% APR for ten years (daily compounding, no payments) leaves you owing about $54,500. Same principal, same rate, simple interest: $17,000. The exponential curve doesn't care which side of the loan you're on.

Try it yourself

Plug your own numbers into the financial calculator. Enter a principal, a rate, and a time horizon, and watch what happens as you slide the compounding frequency from annual to monthly to daily. Then change t from 10 years to 30 — that single edit usually moves the final number by more than any rate change you're realistically going to negotiate. The lever is time, not rate. It always was.

This article is for general education and is not financial advice. See our Terms.