A savings account advertising “5% interest” and one advertising “5% APY” are not necessarily the same thing, and the gap between them adds up to real money over the years. Before you trust any interest rate on a savings account, CD, or loan, there are three numbers worth checking: the nominal rate, the compounding frequency, and the actual annual equivalent rate they produce together.
What compound interest actually does
Compound interest is interest that gets paid on both your original deposit, the principal, and on the interest you’ve already earned. That’s different from simple interest, where only the original principal ever earns anything. Because each round of interest gets reinvested automatically, growth speeds up over time instead of staying flat: exponential rather than linear.
The formula behind it
The standard formula for compound growth is:
A = P(1 + r/n)^(tn)
Where A is the final amount, P is your starting principal, r is the annual nominal interest rate, n is how many times per year the interest compounds (1 for yearly, 12 for monthly, 365 for daily), and t is the number of years.
A real example: $10,000 at 5% over 10 years
Say you deposit $10,000 at a 5% annual rate for 10 years. With simple interest, you’d end up with $15,000, the principal plus $500 a year, flat. With compound interest calculated once a year, the same deposit grows to $16,288.95, because each year’s interest starts earning its own interest. Switch to monthly compounding at the same 5% nominal rate, and it climbs to roughly $16,470. Same advertised rate, nearly $1,470 more than simple interest would give you, and about $180 more than annual compounding, purely from how often the interest gets calculated.
Why the nominal rate isn’t the number that matters
That gap is exactly why many countries require lenders and banks to publish an annual equivalent rate, also called APY, AER, or EAPR depending on where you live, instead of just the nominal rate. In the example above, a 5% nominal rate compounded monthly actually behaves like a 5.116% effective annual rate. That’s the number to compare when shopping between two savings accounts or CDs, not the headline percentage on the ad.
A quick trick for estimating how fast money doubles
If you just want a rough sense of how long it takes an amount to double at a given compound rate, there’s a shortcut that’s been in use since Luca Pacioli wrote it down in 1494: divide 72 by the interest rate. At 5%, that’s 72 / 5 = 14.4 years to roughly double your money. At 8%, it drops to 9 years. It’s an estimate, not an exact figure, but it’s accurate enough to compare offers in your head without a calculator.
Common mistakes people make with compound interest
The most common mix-up is treating every mortgage like a savings account. U.S. mortgages don’t actually compound interest the way a bank account does; they follow an amortization schedule where interest is paid each month rather than capitalized. Canadian mortgages, by contrast, typically compound semi-annually even when payments are made monthly. The other frequent error is ignoring compounding frequency altogether: two accounts with the identical nominal rate can produce meaningfully different balances over 10, 20, or 30 years, just based on how often interest is calculated.
