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Compound Interest

8 min read 5 practice questions
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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Quick check
  8. Study tools
  9. Sources & references

In 30 seconds

is interest earned on both the original amount and the interest already earned — , as OpenStax's Principles of Finance puts it. pays only on the original amount; compound interest pays on the growing total. Year by year the interest keeps earning its own interest, so the balance grows faster the longer it sits. The same engine grows savings — and grows debts. Start early, because compound interest rewards time and punishes delay.

Why this matters

Most people meet compound interest twice: once on the savings side and once on the debt side, and the same math runs both. A savings account that compounds pays interest on interest, so a modest deposit can grow far beyond what simple interest would produce. A credit card that compounds charges interest on interest, so an unpaid balance can balloon. Understanding which side you are on — and how much time changes the outcome — turns a small arithmetic idea into a practical tool for planning. The difference between starting at 25 and starting at 35 can be tens of thousands of dollars, and that difference is pure compounding.

The college version

What compound interest is

The working definition comes from OpenStax's Principles of Finance: compound interest is interest earned in later periods on top of interest earned in earlier periods — put simply, interest that is earned on interest. The SEC's Investor.gov glossary states the same idea in one line: interest paid on and on accumulated interest. CFI's guide adds the practical shape: interest payments made on the sum of the original principal and the previously paid interest. Two halves of the definition matter. First, there is the principal — the original amount deposited or borrowed. Second, there is the accumulated interest — the interest from earlier periods that stays in the account and starts earning its own interest. That second half is the whole idea. In year one, only the principal earns interest. In year two, the principal and year one's interest both earn. The amount earning interest grows every period, and that is why compound growth outpaces simple growth.

Simple versus compound interest

Simple interest pays only on the original principal, every period, forever. Compound interest pays on the growing balance — principal plus previously earned interest. OpenStax puts the boundary plainly: simple interest applies to the first year, compound interest — interest on interest — applies from the second year on. Here is an original worked example. Priya deposits $1,000 at 10% a year for three years. With simple interest, each year pays 10% of $1,000, which is $100, so three years pay $300 and she ends with $1,300. With compound interest, the arithmetic runs on the running balance. Year 1: $1,000 × 0.10 = $100, balance $1,100. Year 2: $1,100 × 0.10 = $110, balance $1,210. Year 3: $1,210 × 0.10 = $121, balance $1,331. Total interest: $331. The extra $31 over the simple-interest $300 is interest earned on interest — the $100 from year one earned $10 in year two, and so on.

The compounding table

The same example reads clearly as a year-by-year table, described in words. Year 1: start $1,000, interest $100 (10% of $1,000), end $1,100. Year 2: start $1,100, interest $110 (10% of $1,100), end $1,210. Year 3: start $1,210, interest $121 (10% of $1,210), end $1,331. Three things to notice. First, the interest row grows every year: $100, then $110, then $121 — each year's interest is 10% of a larger starting balance. Second, the starting balance each year is the previous year's ending balance; nothing is paid out, so nothing stops earning. Third, the growth accelerates: the balance rose $100 in year one, $110 in year two, and $121 in year three. That acceleration is the signature of compounding, and it only becomes more dramatic the longer the table runs.

Compounding frequency

How often interest joins the balance matters. OpenStax's Section 8.4 makes the point with credit card rates: when interest compounds more than once a year, the true annual rate is higher than the appears to be. Here is an original example. Three accounts each offer 12% a year on $1,000, but one compounds annually, one monthly, and one daily. Annual: 12% of $1,000 once, so $1,000 becomes $1,120.00. Monthly: the account earns 1% each month, and each month's interest joins the balance, so $1,000 becomes $1,126.83. Daily: the account earns a tiny slice each day, and it compounds on yesterday's total, so $1,000 becomes $1,127.47. Same stated rate, three different endings. The reason is simple: the more often interest is added, the sooner it starts earning its own interest. Stated simply: more frequent compounding grows faster.

The long game and the debt flip side

Because each year's interest earns interest the next year, small one-time amounts can grow surprisingly large over decades. Original example: a single $500 deposit earning 8% grows to about $1,079 after 10 years, $2,330 after 20, $5,031 after 30, and $10,862 after 40 — the deposit more than doubles in the final decade alone. The same engine runs against borrowers. OpenStax notes the dynamics apply in either direction, and the credit card example is the classic case. A $1,000 balance at 2% per month left unpaid for a year grows to about $1,268 — about $268 of interest, versus $240 if the card charged simple 24%. That extra $28 is interest on interest, charged to the borrower. The honest framing: compound interest rewards time and punishes delay. Starting ten years later with the same $1,000 at 10% means roughly $17,449 at age 65 instead of $45,259 — the missed years are gone, not just postponed.

The honest framing

Compound interest is a mechanism, not a promise. It rewards time because time is what lets interest earn interest; it punishes delay because lost compounding periods never come back. It grows savings and it grows debts with equal enthusiasm, so the same arithmetic that builds a retirement balance also balloons an unpaid credit card balance. The practical lesson is not a get-rich claim but a timing claim: the earlier money starts compounding, the more periods the engine gets to run, and the bigger the ending number — in either direction.

Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Compound interest is interest on interest. Imagine a snowball rolling downhill: it picks up snow, gets bigger, and because it is bigger it picks up even more snow on the next roll. Money works the same way. You put in $100. It earns interest, say $10, so now the ball is $110. Next year the interest is figured on $110, not $100, so it earns $11. The interest itself starts earning interest, and the ball keeps growing faster. Simple interest is the opposite: it is like paying the same flat amount every year no matter how big the pile gets.

Picture it like this

Think of compound interest as a snowball rolling down a long hill. The snow it picks up makes it bigger, and a bigger snowball picks up more snow with every turn. Money does the same: the interest it earns makes the balance bigger, and a bigger balance earns more interest the next period. Give the snowball a long hill and a little snow becomes a lot.

Where the picture stops working

The snowball only grows if the hill keeps going and nothing melts. In the same way, compounding only works while the money stays invested at a positive rate — take the interest out, or the rate drops to zero, and the snowball stops growing. And the analogy hides the debt side: a snowball rolling the other way, onto the borrower, grows against you.

Worked example

Priya deposits $1,000 in an account that pays 10% interest a year and leaves it for three years. With simple interest, the math is flat: 10% of $1,000 is $100 each year, so three years pay 3 × $100 = $300, and she ends with $1,300. With compound interest, each year's interest is figured on the running balance. Year 1: $1,000 × 0.10 = $100, so the balance is $1,100. Year 2: $1,100 × 0.10 = $110, so the balance is $1,210. Year 3: $1,210 × 0.10 = $121, so the balance is $1,331. Her total interest is $331 — $31 more than simple interest would have paid. The extra $31 is interest earned on interest: the $100 earned in year one earned $10 in year two, and the $210 earned by the end of year two earned $21 in year three. Nothing was added beyond the original $1,000; the growth came from the interest itself earning.

Key takeaway

Compound interest is interest on interest: it pays on the original amount and on previously earned interest, so it rewards time and punishes delay — growing savings and debts alike the longer it runs.

Quick check

3 questions here, of 5 in this lesson’s practice set. Answers stay hidden until you check.

Question 1 of 3foundational

Compound interest is interest earned on which of the following?

Choose an answer, then check it.
Question 2 of 3intermediate

Priya deposits $1,000 at 10% interest and leaves it for three years. With compound interest, what is her balance at the end of year 3?

Choose an answer, then check it.
Question 3 of 3advanced

Three accounts each pay 12% a year on $1,000, but they compound annually, monthly, and daily. Which account ends the year with the largest balance?

Choose an answer, then check it.
Practice all 5

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Study tools & related lessonsYou’ll learn to · Common mistakes · Easily confused · Key vocabulary · Related

You’ll learn to

  • Define compound interest as interest earned on both the original amount and previously earned interest, using the working definition attributed to OpenStax's Principles of Finance and the SEC's Investor.gov glossary.
  • Distinguish compound interest from simple interest: simple pays only on the principal; compound pays on the growing balance.
  • Work an original three-year example at 10% on $1,000, showing the arithmetic: simple gives $300 of interest, compound gives $331.
  • Read a year-by-year compounding table in words — year, start, interest, end — and explain where each year's interest comes from.
  • State simply that more frequent compounding (monthly or daily rather than annual) makes money grow faster at the same stated rate.
  • Explain the honest framing: compound interest rewards time and punishes delay — the same engine that grows savings grows debt, and small one-time amounts can grow surprisingly large over decades.

Common mistakes

  • Treating compound interest as simple interest — assuming every year pays the same flat amount on the original deposit.

    After the first year, interest is figured on the running balance, not the original amount. Each year's interest is 10% (or whatever the rate is) of a larger starting balance.

  • Comparing accounts only by the stated rate and ignoring how often interest compounds.

    At the same stated rate, monthly or daily compounding beats annual compounding because interest joins the balance sooner and starts earning its own interest.

  • Thinking compound interest only helps savers and never touches borrowers.

    The same engine runs in reverse on debt: an unpaid credit card balance compounds monthly, so interest is charged on accumulated interest.

  • Assuming that delaying by a few years only costs a few years of flat interest.

    Delay costs the compounding periods themselves — the interest those years would have earned keeps earning for decades. Starting later means the missed years are gone, not postponed.

Easily confused

Simple interest vs. Compound interest

Simple interest pays only on the original principal each period; compound interest pays on the principal plus previously earned interest, so the balance grows faster over time.

Annual compounding vs. Monthly or daily compounding

At the same stated rate, more frequent compounding adds interest to the balance sooner, so the balance ends the year slightly larger.

Compound interest on savings vs. Compound interest on debt

The mechanism is identical; it grows a saver's balance and grows a borrower's unpaid balance with equal enthusiasm.

Key vocabulary

Compound interest
Interest earned on both the original amount and the interest already earned in earlier periods — interest on interest, as OpenStax's Principles of Finance defines it.
Principal
The original amount of money deposited or borrowed, before any interest is added.
Simple interest
Interest paid only on the original principal each period, never on previously earned interest.
Interest on interest
The interest earned in a later period on interest earned in earlier periods; the engine that makes compound growth accelerate.
Compounding frequency
How often interest is added to the balance during a year — for example, annually, monthly, or daily.
Compounding table
A year-by-year list showing the starting balance, the interest earned, and the ending balance for each period.
Stated rate
The interest rate named on the account or loan, which can understate the true annual cost or gain when compounding happens more than once a year.
Time horizon
How long money stays invested or borrowed; the longer the horizon, the more compounding periods operate.

Sources & references

  1. Principles of Finance, Section 7.2: Time Value of Money (TVM) Basics — OpenStax, Rice University
  2. Principles of Finance, Section 8.4: Stated versus Effective Rates — OpenStax, Rice University
  3. Compound Interest (Investor.gov glossary) — U.S. Securities and Exchange Commission, Investor.gov
  4. Compound Interest — Corporate Finance Institute (CFI)

EliExplains lessons are original prose written from the open, credible references above. See Copyright & Licensing.

Researched 2026-08-21

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