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The Compound Interest Formula

Compound interest earns interest on both your original principal and on previously accumulated interest. The formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest compounds per year, and t is the number of years. With regular contributions, the formula becomes: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)].

Simple vs. Compound Interest

Simple interest only earns returns on your original principal. At 5% simple interest, $10,000 earns exactly $500 per year — $5,000 after 10 years. With compound interest (compounded monthly), the same $10,000 earns $6,470 — that's $1,470 more, entirely from interest earning interest. Warren Buffett built his $100+ billion fortune largely through compound returns, starting at age 11.

Daily vs. Monthly vs. Annual Compounding

More frequent compounding means slightly more interest, because each compounding period adds interest that then earns interest in subsequent periods. However, the differences are relatively small for savings accounts.

For most savers, the difference between monthly and daily compounding is negligible — about $17 on a $10,000 deposit over 10 years at 5%. Where compounding frequency really matters is with larger balances and higher rates: on a $100,000 balance at 8%, daily vs. annual compounding produces a $2,000+ difference over 10 years.

Why Consistent Saving Matters More Than Rate

Regular contributions have a far greater impact on your savings outcome than the interest rate, especially in the first 10–15 years. Vanguard research found that investors who consistently contributed to their accounts — regardless of market conditions — outperformed those who tried to time the market by an average of 1.5 percentage points per year.

How Contributions Compound

Consider someone saving $500/month at 5% APY: after 10 years, they'll have contributed $60,000 in principal but accumulated $77,641 total — that's $17,641 in interest. After 30 years, contributions of $180,000 grow to $416,129 — more than $236,000 in earned interest. The interest earned exceeds the total contributions after approximately year 20.

The Rule of 72

The Rule of 72 is a quick mental math shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money. At 6% interest, money doubles in 72 ÷ 6 = 12 years. At 8%, it doubles in 9 years. At 4%, it takes 18 years. This rule is accurate within 1% for rates between 4–15%.

Why Nominal Returns Mislead

If your savings earn 5% annually but inflation is 3%, your real return is only about 2%. The Bureau of Labor Statistics reports that the average U.S. inflation rate from 2000–2023 was 2.5%, but spiked to 9.1% in June 2022 — the highest in 40 years. Failing to account for inflation can make savings projections overly optimistic.

Inflation-Adjusted Purchasing Power

$100,000 saved today will only buy the equivalent of about $74,400 in goods after 10 years of 3% inflation — and just $55,400 after 20 years. This is why investment advisors consistently recommend diversifying into assets that outpace inflation: historically, the S&P 500 has returned approximately 10.5% annually (7.5% after inflation), while bonds have returned about 5% (2% after inflation) according to NYU Stern School of Business data spanning 1928–2023.