Compound Interest Calculator
Project compound-interest growth from deposits and a nominal rate, then test how timing, taxes, fees, inflation, and a goal change the outcome.{{ summaryTitle }}
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Money compounds when credited interest remains in the balance and can earn interest in later periods. The first few credits may look small, but the base grows over time. New deposits add another source of growth because each contribution begins its own compounding path from the month it arrives.
A quoted annual rate does not fully describe that path. The nominal rate is divided or transformed according to the compounding convention, producing an effective one-year yield. Contribution timing also matters: money added at the beginning of a month receives that month's growth, while an end-of-month deposit does not.
- Principal
- The opening balance available before recurring deposits begin.
- Nominal annual rate
- The stated rate before compounding frequency is applied.
- Effective annual yield
- The one-year return implied by the nominal rate and compounding convention.
- Real balance
- The future balance discounted by assumed inflation to express estimated purchasing power.
Time, deposits, rate, and cost assumptions can pull the result in different directions. A longer horizon gives compounding more room, but taxes on credited interest, percentage fees, and fixed monthly fees reduce the amount left to grow. Inflation does not remove dollars from the account; it changes what the projected dollars may buy.
| Change | Typical effect | Reason |
|---|---|---|
| Earlier contributions | Higher ending balance | Each deposit receives more monthly growth periods |
| More frequent compounding | Slightly higher effective yield at the same positive nominal rate | Interest is credited to the base sooner |
| Taxes or fees | Lower nominal balance | Less credited growth remains invested |
| Inflation | Lower real balance | Future currency buys less under the assumption |
A projection is most useful for comparing scenarios and testing a savings goal. It is not a forecast of market returns or a promise from a bank. Real products may use daily balances, tiered or changing rates, maturity rules, contribution limits, withdrawal penalties, tax treatments, and institution-specific rounding.
A precise-looking final number can hide weak assumptions. Test several plausible rates, contribution amounts, and fee levels. When a target is important, leave a buffer rather than treating the first modeled month above the goal as guaranteed.
How to Use This Tool:
Enter the account assumptions as they are stated, especially the nominal rate and deposit timing, before testing taxes, fees, inflation, or a target.
- Enter the opening balance and recurring deposits. Use zero for either source when the plan is lump-sum-only or contribution-only.
- Set the nominal annual rate, compounding frequency, and horizon. Do not substitute annual percentage yield for a nominal rate. The combined horizon must be from 1 through 600 months.
- Choose contribution timing. Add annual contribution and contribution growth only when the plan includes them; the annual amount is spread evenly across months.
- Add taxes, inflation, and fees as scenario assumptions. Use zero when an adjustment does not apply, and verify the account's real treatment before relying on the result.
- Review ending balance, real balance, invested amount, interest, fees, and goal timing. Compare the growth path with the assumption review before changing one input at a time.
Interpreting Results:
Ending balance is the modeled account value after contributions, credited interest, taxes on that interest, and fees. Real ending balance discounts the same nominal balance by inflation. Total invested is principal plus contributions, so the difference between ending balance and invested money is not the same as gross interest when fees are present.
- Check Effective annual yield against the selected nominal convention; it is not necessarily the account's disclosed annual percentage yield.
- Goal timing is the first modeled month at or above the target. It does not include a safety margin for changing rates, missed deposits, taxes, or withdrawals.
- If fees approach or exceed credited interest, inspect Total fees and the growth path rather than relying on the final balance alone.
Technical Details:
The model converts the selected nominal annual convention into an equivalent monthly rate, then advances the balance one month at a time. This preserves the selected annual yield while supporting monthly deposits, partial-year horizons, and monthly fees.
Formula Core
For a nominal annual rate r compounded n times per year, the implied annual yield A is:
Continuous compounding uses the exponential limit, and every convention is converted to a monthly rate i.
Each month applies any beginning contribution, after-tax interest, percentage and fixed fees, then any end contribution.
The fixed monthly contribution and one-twelfth of the annual contribution are combined. That combined amount grows at the entered annual contribution-growth rate after each completed 12-month block.
| Symbol | Meaning |
|---|---|
| r | Nominal annual rate as a decimal |
| n | Compounding periods per year |
| i | Equivalent monthly rate |
| t | Tax share applied to credited interest |
| f | Annual percentage fee as a decimal |
| Bm | Balance at the start of month m |
| C | Monthly contribution placed at the selected timing |
Inflation changes the purchasing-power comparison without changing the nominal account balance.
Intermediate values keep full floating-point precision. Currency, percentages, and dates are rounded only for display. The model uses USD labels and a general monthly recurrence rather than a bank-specific daily-balance or day-count convention.
Limitations:
This projection is educational and is not financial, investment, tax, or legal advice.
- Rates are held constant. Market returns, variable account rates, and sequence-of-return risk are not modeled.
- The tax field applies one percentage to each month's credited interest; it does not model tax brackets, account type, realized gains, deductions, or filing rules.
- Fees are a monthly percentage charge plus a fixed monthly amount. Tiered fees, minimum balances, transaction charges, and penalties need a separate review.
- Inflation is a constant annual assumption, not a forecast of a particular consumer price index.
Worked Examples:
Two years of annual compounding
A $1,000 balance at a 5% nominal rate compounded annually, with no deposits, taxes, fees, or inflation, becomes $1,050 after one year and $1,102.50 after two years. The second year's $52.50 includes interest earned on the first year's $50.
A target reached by deposits
With a $1,000 opening balance, a 0% rate, and $100 deposited at each month-end, the balance reaches a $2,000 target in month 10 and ends month 12 at $2,200. The example isolates contribution timing because no interest or fee changes the result.
References:
- How does compound interest work?, Consumer Financial Protection Bureau, 2023.
- Compound Interest Calculator, U.S. Securities and Exchange Commission.
- Appendix A to Regulation DD: Annual Percentage Yield Calculation, Consumer Financial Protection Bureau.