How Does Compound Interest Actually Work? A Real Numbers Example

Direct answer: Compound interest is interest earned on interest, not just on the original amount. The U.S. Securities and Exchange Commission’s own investor-education example shows it concretely: $100 invested at 5% annual interest becomes $105 after year one, $110.25 after year two (5% of $105, not just 5% of the original $100), and almost $340 after 25 years, without ever adding another dollar to the account.

The Actual Math, Not Just the Concept

It’s easy to nod along to “interest on interest” without seeing why it matters, so here’s the real calculation. Start with $100 at 5% annual interest. Year one: $100 × 5% = $5 in interest, giving $105 total. Year two is where compounding actually shows up: instead of earning another flat $5, the account now earns 5% of $105, which is $5.25, bringing the total to $110.25. That extra 25 cents came from interest earned on the previous year’s interest, not on the original $100. It’s a small difference in year two. Over 25 years, with the same $100 never added to, that same effect compounds the balance to almost $340, more than triple the starting amount, from growth alone.

Why the Effect Gets Bigger the Longer Money Sits

The reason compound interest rewards starting early more than starting with more money is directly visible in the math above: the “interest on interest” effect needs time to actually build, since each year’s extra growth comes from the balance the account has already reached. A dollar invested today has more compounding cycles ahead of it than the same dollar invested five years from now, which is why the gap between an early start and a late start tends to widen, not narrow, the longer both accounts are left alone.

Where Compound Interest Applies Beyond a Simple Savings Example

The SEC’s example uses a flat savings-account-style rate for clarity, but the same “interest on interest” mechanism is what makes retirement accounts, 401(k)s, IRAs, and taxable brokerage accounts, grow the way they do over decades, not just simple interest-bearing savings accounts. It’s also worth understanding in reverse: the same compounding math working in a saver’s favor works against a borrower carrying high-interest credit card debt, where unpaid interest gets added to the balance and then itself starts accruing interest.

What This Means for a Family’s Real Financial Decisions

The practical takeaway is that the exact numbers matter less than the shape of the curve: growth from compound interest is genuinely slow in the early years and genuinely faster in the later years, using the same rate the entire time. That’s the real, mathematical reason “start now, even with a small amount” is more than a generic platitude, the SEC’s own $100 example shows the effect is real and measurable, even though it takes real years to become visible.

Sources: The $100-at-5%-interest example (year one, year two, 10-year, and 25-year figures) sourced directly from U.S. Securities and Exchange Commission, Investor.gov, “What is compound interest?” Verified 2026-08-10.