Compound Interest vs Simple Interest: Examples, APY and the Rule of 72

The same deposit, two kinds of interest

Put $10,000 away for 30 years at 5% a year:

Simple interest            $25,000.00
Compounded annually        $43,219.42
Compounded monthly         $44,677.44
Compounded daily           $44,812.29

Simple interest adds the same $500 every year. Compounding adds $500 in the first year, but by year 30 a single year’s interest is over $2,000, because it is earned on a much larger balance. Notice that the jump from simple to compound is huge, while the jump from monthly to daily compounding is small — frequency matters far less than time.

APR, APY and comparing accounts

A savings account quoting “5% compounded monthly” actually earns 5.12% over a year, and daily compounding earns 5.13%. That effective yearly figure is the annual percentage yield (APY). Because APY already includes compounding, it is the fair way to compare savings accounts and certificates of deposit.

Loans quote an annual percentage rate (APR), which in the US includes certain fees but not the effect of compounding. When comparing loans, compare APRs; when comparing savings, compare APYs.

The Rule of 72

To estimate how long money takes to double, divide 72 by the annual percentage rate. It is surprisingly accurate across normal rates:

Rate   Rule of 72   Exact
4%     18.0 years   17.67 years
6%     12.0 years   11.90 years
8%      9.0 years    9.01 years
12%     6.0 years    6.12 years

It works because the exact doubling time is ln 2 ÷ ln(1 + rate), and 72 happens to approximate 100 × ln 2 (69.3) while correcting for the curve at typical rates. The same rule works for inflation: at 3% a year, prices double in about 24 years.

Compounding against you: credit cards

Credit cards compound too, usually on a daily balance. Take a $5,000 balance at 24% APR with no new spending. Paying $150 a month takes about 56 months to clear and costs roughly $3,300 in interest. Paying $300 a month clears it in about 21 months for roughly $1,100 of interest (figures computed with monthly compounding; daily compounding adds slightly more). Doubling the payment cuts the interest by about two-thirds, because each extra dollar stops compounding immediately.

Minimum payments are designed to keep balances alive for years. If you carry several debts, paying the highest-rate one first (the “avalanche” method) costs the least overall.

Making compounding work for you

• Start early: time is the biggest lever. Contributions made in your twenties have far longer to compound than larger ones made later.
• Reinvest returns: dividends and interest that are withdrawn stop compounding.
• Watch fees: a 1% annual fee on a 7% return leaves 6%, which over 30 years ends about a quarter lower.
• Think in real terms: subtract inflation to see growth in today’s money. A 5% return with 3% inflation is roughly 2% real growth.

Use the compound interest calculator to try your own numbers, including monthly additions. Investment returns are never guaranteed; this guide explains the arithmetic and is not investment advice.

Inflation: compounding in reverse

Inflation compounds against cash. At 3% a year, $100 buys what $74.41 buys today after 10 years, $55.37 after 20 and $41.20 after 30. Money left in an account paying less than inflation is shrinking in real terms even while the balance grows. That is why long-term savings goals are usually planned with a real return — the nominal rate minus inflation — rather than the headline rate.

Continuous compounding and the limit of frequency

If interest compounded infinitely often, the formula becomes FV = P × e^(r × t), where e ≈ 2.71828. For $10,000 at 5% over 30 years that is $44,816.89 — only $4.60 more than daily compounding. Frequency has a ceiling; time and rate do not. Continuous compounding appears mostly in finance theory and option pricing, but it is a useful reminder that chasing “daily” versus “monthly” compounding matters far less than starting earlier or finding a better rate.

Regular contributions: where most growth comes from

Most people build savings through regular deposits rather than one lump sum. At an assumed 7% average annual return, $300 a month grows to about $365,991 after 30 years, from $108,000 of contributions. Doubling the contribution to $600 a month gives about $731,983 over the same 30 years. Keeping $300 a month but starting ten years earlier — 40 years in total — gives about $787,444. Starting a decade earlier beats doubling the amount, because the earliest deposits compound the longest.

Real returns vary from year to year, and these figures are illustrations rather than forecasts. The compound interest calculator handles a starting balance plus monthly additions, so you can test your own plan.

Taxes on interest and gains

In a regular taxable account, interest is usually taxed each year, which removes part of the balance before it can compound. Tax-advantaged retirement accounts let growth compound without annual tax, which is a large part of their long-term advantage. Rules differ by country, so check how your own accounts are taxed before comparing projections.

Common projection mistakes

• Using a nominal return for a goal set in today’s money — subtract inflation first.
• Assuming a constant return: the order of good and bad years matters once you start withdrawing.
• Ignoring fees, which compound as relentlessly as returns.
• Forgetting that contributions often rise with income; a projection with flat contributions understates what most savers achieve.