Compound Interest Calculator

When to Use Each Variable

• Solve for Final Amount (A) — when you have a starting deposit and want to project the balance at the end of a savings or investment horizon.
• Solve for Principal (P) — when you have a future target (college fund, retirement nest egg) and need to back out how much to deposit today.
• Solve for Rate (r) — when you observe a growth from P to A over a known horizon and want the implied constant annual rate.
• Solve for Time (t) — when you want to know how many years a deposit needs to compound at a given rate to reach a target.

Key Concepts

Two ideas matter most. First, compounding frequency affects how fast P grows: at the same nominal annual rate, daily compounding outperforms annual compounding because interest is added (and starts earning interest) more often. The limit n → ∞ is continuous compounding, A = P·e^(rt), which puts a hard ceiling on how much more frequent compounding can buy you. Second, compound interest differs from simple interest in that simple interest computes only P × r × t — it ignores interest earning interest, so it underestimates growth on multi-year horizons by an amount that itself grows exponentially with t. A related shortcut is the Rule of 72: the doubling time at rate r% is roughly 72/r years (e.g., 6% doubles in about 12 years). It's a rule of thumb derived from ln(2)/ln(1 + r/100) for small r and is accurate to within a percent or two for rates between 4% and 12%.

Applications

• Savings accounts and money-market funds — project the balance under quoted APY or APR
• Certificates of deposit (CDs) — verify the maturity value advertised by the bank
• Retirement accounts (IRAs, 401(k)s) — long-horizon compound growth of a lump-sum rollover
• Mortgage and loan amortization — the same compound-amount factor underlies amortization schedules
• Inflation modeling — apply an annual inflation rate to project future prices or purchasing power
• Bond pricing — zero-coupon bonds are priced as the present value of a future amount under compound discounting
• Exponential growth in biology and epidemiology — the same equation describes population growth, bacterial doubling, and the early phase of an epidemic curve

Common Mistakes

• Confusing nominal annual rate with effective annual rate (EAR). A nominal 6% APR compounded monthly is an EAR of about 6.17%; quoting one when the other is required produces a small but real error in long-horizon calculations.
• Mixing time units — using an annual rate with monthly time or vice versa. Either keep everything annual (r is annual, t in years, n = periods/year) or restate the rate to match the time basis.
• Forgetting to divide r by n inside the parentheses. The per-period rate is r/n, not r — using the annual rate directly with monthly periods enormously overstates the result.
• Entering the rate as a percent instead of a decimal in formulas that expect a decimal. This calculator accepts a percent for convenience and converts internally, but textbook formulas use decimals.
• Ignoring tax drag in taxable accounts. The pre-tax compounded balance overstates after-tax wealth; for taxable accounts, use the after-tax rate of return.
• Assuming simple interest and compound interest converge — they diverge faster as t and r grow. Over a 30-year horizon, compounding can roughly double the simple-interest result.