The power of compound interest
Compound interest means earning interest on your interest, not just on your original principal. Over long periods, this creates an exponential growth curve — the same reason Einstein allegedly called it "the eighth wonder of the world."
Why compounding frequency matters
Daily compounding earns slightly more than monthly, which earns more than annual. For a $10,000 deposit at 7% annual rate over 30 years: annual compounding → $76,123; monthly → $81,165; daily → $81,645. The difference grows with the amount and time, but monthly compounding captures most of the benefit of daily compounding.
The Rule of 72
A quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years to double your money. At 7%: 72/7 ≈ 10.3 years. At 10%: 72/10 = 7.2 years. At 4%: 72/4 = 18 years. This rule works for compound growth of any kind — investments, inflation, population growth.
Monthly contributions make a dramatic difference
Starting with $10,000 and earning 7% for 30 years with no contributions → $76,123. Adding $500/month → $681,752. The contributions account for $180,000 in actual money deposited; the remaining $501,752 is pure compound growth. This illustrates why starting early matters far more than starting big.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt) where A = final amount, P = principal, r = annual rate (decimal), n = compounds per year, t = years. With regular contributions, the formula extends to include the future value of an annuity. This calculator handles both.
What is a realistic interest rate to use?
High-yield savings accounts: 4–5% (2026). CDs: 3.5–5%. US bond funds: 4–5%. Total US stock market index funds: historical average ~10% nominal, ~7% after inflation. It is generally wise to use conservative projections — 5–7% for diversified portfolios — when planning for long-term goals.
Does this account for inflation?
No — this is a nominal return calculator. To estimate real (inflation-adjusted) returns, subtract the expected inflation rate from your interest rate. Historically, US inflation averages about 3%, so a 7% nominal return is roughly 4% real. The calculator works in nominal dollars.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the stated annual rate before compounding. APY (Annual Percentage Yield) is the effective rate after accounting for compounding — always higher than APR for the same account. Banks are required to display APY. When comparing savings accounts, use APY.