Interest Calculator
Calculate compound interest with daily, monthly, quarterly, or annual compounding. Add regular contributions, apply a tax rate on interest earnings, and adjust for inflation to see the real purchasing power of your investment. Includes a year-by-year growth table and the Rule of 72 to estimate doubling time.
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How It Works
Compound interest applies the rate to both principal and accumulated interest. The formula A = P(1 + r/n)^(nt) calculates the final amount where P is principal, r is annual rate, n is compounding frequency, and t is years.
A = P(1 + r/n)^(nt)$10,000 at 5% monthly for 10yr = $16,470.09Each contribution also earns compound interest from the moment it is added. The total future value combines the principal growth and the future value of all periodic contributions using the annuity formula.
A = P(1+r/n)^(nt) + PMT × [(1+r/n)^(nt) - 1] / (r/n)$10K + $200/mo at 7% for 20yr = $170,000+APY accounts for compounding within the year. Daily compounding at 5% APR yields 5.127% APY. The gap between APR and APY increases with higher rates and more frequent compounding.
APY = (1 + r/n)^n - 15% APR daily = 5.127% APY; 5% APR annual = 5.000% APYInterest income is taxed at ordinary income rates. The calculator deducts the tax rate from total interest earned to show the after-tax balance. For long time horizons, tax-advantaged accounts like IRAs and 401(k)s significantly outperform taxable accounts.
After-tax interest = Total Interest × (1 - Tax Rate)$5,000 interest at 22% tax = $3,900 after-taxInflation erodes purchasing power over time. The inflation-adjusted value divides the nominal final balance by (1 + inflation rate)^years to show what the money is worth in today's dollars.
Real Value = Nominal Balance / (1 + inflation)^t$76,000 in 30yr at 3% inflation = $31,300 today's valueDivide 72 by the interest rate to estimate years to double. At 6% it takes 12 years; at 9% it takes 8 years. The rule slightly overestimates at very high or low rates but is accurate for 6% to 10%.
Years to double ≈ 72 / Interest Rate (%)8% rate: 72/8 = 9 years to doubleQuick Reference
Common examples — verify instantly above.
$10K at 5%, 10yr
Monthly compounding
$16,470
$10K at 7%, 30yr
Monthly compounding
$76,123
+$200/mo
$10K at 7% for 20yr
$171,400
Rule of 72
At 6% rate
Doubles in 12 years
APY from 5% APR
Monthly compounding
5.116% APY
APY from 5% APR
Daily compounding
5.127% APY
Tax impact
$5K interest at 22% bracket
$3,900 after tax
Inflation adjust
$76K in 30yr at 3%
$31,300 today's value
Tips & Shortcuts
Start investing as early as possible. The difference between starting at 25 versus 35 with the same monthly contribution can exceed $200,000 at retirement due to compound growth.
Use daily or monthly compounding accounts over annual compounding for savings. The difference is small annually but compounds to meaningful amounts over decades.
Compare APY — not APR — when evaluating savings accounts, CDs, and money market accounts. APY already accounts for compounding.
Use the inflation adjustment to see if your investment is truly growing in real terms. A 6% nominal return at 4% inflation is only 2% real growth.
Tax-advantaged accounts (IRA, 401k, HSA) eliminate the tax drag on interest income. The same investment inside an IRA significantly outperforms a taxable account over 20+ years.
Even a small interest rate difference compounds dramatically. At 30 years, 5% versus 7% on $20,000 means $86,439 versus $152,245 — a $65,806 difference.
Common Mistakes to Avoid
Confusing APR with APY when comparing savings products
APY includes compounding and is always equal to or higher than APR. Always use APY for comparing savings accounts. A 4.95% APY is better than 5% APR compounded annually.
Ignoring inflation when planning long-term savings
$1 million in 30 years is worth about $412,000 in today's purchasing power at 3% inflation. Plan for both nominal and real returns.
Not accounting for taxes on interest income in taxable accounts
For investors in the 22-32% tax bracket, after-tax interest income is significantly lower. Use tax-advantaged accounts for long-term savings whenever possible.
Withdrawing interest instead of letting it compound
Reinvesting interest is the source of compound growth's power. Withdrawing annually turns compound interest into simple interest, dramatically reducing long-term returns.
Waiting to invest until you have a large sum
Dollar-cost averaging with regular contributions typically outperforms waiting. The earlier compounding starts, the more powerful it becomes — even with small amounts.
Comparing nominal rates across different compounding frequencies
Always convert to APY for fair comparison. A bank offering 4.5% compounded daily beats one offering 4.5% compounded annually by 0.06% in effective yield.
Frequently Asked Questions
Compound interest is interest calculated on both the initial principal and all previously accumulated interest. Unlike simple interest which applies only to the principal, compound interest creates exponential growth because each period's interest becomes part of the base for the next period.
More frequent compounding produces higher effective yields. Daily compounding on 5% APR yields an APY of 5.127%, while annual compounding at the same APR yields exactly 5.0%. The difference compounds significantly over decades.
The Rule of 72 estimates how long it takes to double an investment. Divide 72 by the annual interest rate. At 6%, money doubles in approximately 12 years. At 8%, it doubles in about 9 years. The rule works best for rates between 6% and 10%.
Interest income is taxable at ordinary income rates in the US. If your marginal tax rate is 22% and you earn $5,000 in interest, you keep only $3,900. Over long periods, taxes can reduce the final balance by 20% to 30% for investors in higher brackets.
APR (Annual Percentage Rate) is the nominal rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding is applied. At 5% APR compounded monthly, the APY is 5.116%. Always compare APY when evaluating savings accounts or CDs.
Regular contributions dramatically accelerate wealth accumulation. $10,000 invested at 7% for 30 years grows to $76,123. Adding just $200 per month grows it to $302,834 — four times more. The compounding of contributions creates a snowball effect.
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