Understanding Compound Interest (And Why It's Called the Eighth Wonder)
How compound interest actually works, a worked savings example, and what to look for in a high-yield savings account.
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Compound interest is the mechanism behind almost every long-term savings and investment strategy. Understanding it changes how you think about both saving early and paying down debt.
The formula
A = P × (1 + r/n)^(n × t)
Where A is the final amount, P is the principal (starting amount), r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.
Worked example
Suppose you deposit $5,000 into an account paying 5% annual interest, compounded monthly, for 10 years:
- P = 5,000
- r = 0.05
- n = 12
- t = 10
A = 5,000 × (1 + 0.05/12)^(12 × 10) ≈ 5,000 × 1.647 ≈ $8,235
Notice the account earned about $3,235 in interest — more than a simple-interest calculation would produce, because each month's interest starts earning interest of its own.
Why compounding frequency matters
More frequent compounding (daily vs. monthly vs. annually) produces a slightly higher return at the same stated annual rate, because interest is added to the balance — and starts earning its own interest — sooner. The difference is usually modest for typical savings rates, but it adds up over long time horizons.
What to look for in a savings account
When comparing accounts, the Annual Percentage Yield (APY) already accounts for compounding frequency, so it's a fairer way to compare two accounts than the stated interest rate alone. A handful of online banks and fintech apps consistently offer notably higher APYs than traditional brick-and-mortar banks on standard savings accounts — it's worth comparing a few before parking a large balance in a low-yield account you've had for years out of habit.
Try the math yourself
Our percentage calculator is useful for sanity-checking a single year's interest or a rate comparison, and our unit converter can help if you're converting between currencies or measurement units used in a broader financial comparison.