Compound Interest Calculator
See exactly how investments grow with compound interest — the most powerful force in personal finance. Compare annual, monthly, and daily compounding frequencies, and discover how regular monthly contributions dramatically multiply long-term wealth.
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How It Works
Future value = P(1+r/n)^(nt) where P is principal, r is annual rate, n is compounding periods per year, and t is years. More frequent compounding slightly increases growth because interest is earned on interest more often.
FV = P(1 + r/n)^(nt)$10K at 7% for 30yr, monthly compounding = $81,745Adding regular contributions: total FV equals lump sum FV plus contribution FV = PMT x [(1+r/n)^(nt) - 1] / (r/n). The contribution component compounds exponentially, making consistent investing extremely powerful.
FV = lump sum FV + PMT x [(1+r/n)^(nt) - 1] / (r/n)$10K + $500/mo, 7%, 30yr = $612,285 total valueSimple interest applies only to the original principal: A = P(1 + rt). No compounding occurs. Used for short-term loans, promissory notes, and some bonds where the borrower pays only on the original amount.
A = P(1 + rt)$10K, 5%, 3 years simple interest = $1,500 total interestA = Pe^(rt) where e is Euler's number approximately 2.71828. Represents the mathematical limit of compounding infinitely often. Daily compounding is over 99.9% as effective as continuous, so the practical difference is minimal.
A = P x e^(rt)$10K, 7%, 30yr continuous compounding = $82,270EAR = (1 + r/n)^n minus 1. Converts any APR to its equivalent annual yield after compounding effects. Essential for comparing savings accounts, CDs, and investment products with different compounding schedules.
EAR = (1 + r/n)^n - 112% APR compounded monthly = 12.68% effective annual yieldDivide 72 by the annual interest rate for a quick estimate of doubling time. The exact formula is ln(2) divided by ln(1+r). The Rule of 72 is accurate within a few months for rates between 5% and 15% per year.
Doubling time approximately 72 / annual_rate_percentAt 8% annual rate: 72 / 8 = 9 years to double your moneyQuick Reference
Common examples — verify instantly above.
7% for 30 years
$10,000 lump sum
$76,123 final value
Monthly compounding
$10K, 7%, 30yr
$81,745 final value
Daily compounding
$10K, 7%, 30yr
$81,997 final value
With contributions
$10K + $500/mo, 7%, 30yr
$612,285 final value
Rule of 72 at 7%
Years to double money
Approximately 10.3 years
Simple interest
$10K, 5%, 3 years
$1,500 interest earned
EAR at 12% APR
Monthly compounding
12.68% effective rate
Continuous 7%
$10K for 30 years
$82,270 final value
Tips & Shortcuts
Start investing as early as possible. Even a 5-year head start can mean hundreds of thousands more at retirement due to compound growth.
The compounding frequency matters far less than the rate and time period. Focus on finding the best return rate rather than daily vs monthly compounding.
Tax-advantaged accounts like 401k and IRA allow compound interest to work without annual tax drag, dramatically increasing long-term returns.
Reinvesting dividends is compounding in action — your dividends buy more shares, which pay more dividends, which buy more shares.
Inflation also compounds at roughly 3% per year, halving purchasing power in 24 years. Your investment return must exceed inflation for real wealth growth.
Always use APY rather than APR to compare savings accounts, CDs, and investment products with different compounding frequencies.
Common Mistakes to Avoid
Waiting to start investing
The biggest mistake is delaying. $5,000 invested at age 25 at 7% grows to $75,000 by age 65. The same amount invested at age 35 grows to only $38,000 — the 10-year delay costs $37,000.
Comparing APR across products with different compounding periods
A 6% APR compounded daily is better than 6% compounded annually. Always convert to APY to compare financial products on equal terms.
Ignoring investment fees and expense ratios
A 1% annual fund fee reduces a 7% return to 6% effectively. Over 30 years on $100,000 that fee costs over $130,000 in lost compounding returns.
Withdrawing principal from compound investments early
Withdrawing principal resets your compounding base. Even taking out a small amount early has disproportionately large long-term costs due to lost compounding time.
Assuming past rates continue indefinitely
Historical stock market returns average about 7% after inflation but any individual year can vary dramatically. Use conservative estimates for long-term financial planning.
Forgetting about inflation eroding real returns
A 5% nominal return with 3% inflation is only a 2% real return in purchasing power. Always think in real (inflation-adjusted) terms for long-term planning.
Frequently Asked Questions
Compound interest is interest calculated on both the initial principal AND all accumulated interest from prior periods. Unlike simple interest which only applies to the original principal, compound interest grows exponentially because your earnings themselves earn returns.
More frequent compounding produces slightly more growth. $10,000 at 7% for 30 years grows to $76,123 with annual compounding, $81,745 with monthly compounding, and $81,997 with daily compounding. The difference is real but smaller than most people expect.
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 7% annual return, money doubles in approximately 72 divided by 7 which equals 10.3 years. This approximation works best for rates between 5% and 15%.
APR is the stated interest rate before compounding effects. APY is the effective annual yield after all compounding. A 12% APR compounded monthly produces a 12.68% APY. Always use APY to compare products with different compounding frequencies.
Regular contributions dramatically accelerate wealth building. Adding $500 per month to a $10,000 investment at 7% for 30 years grows to $612,000 compared to $76,000 with no contributions. Starting early and contributing consistently is the most powerful wealth-building strategy.
Continuous compounding is the mathematical limit of compounding infinitely often, described by the formula A = Pe^(rt). It represents the theoretical maximum return from compounding. Daily compounding achieves over 99.9% of the theoretical maximum.
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