Menu

Saving and growth

Compound interest calculator

Estimate how one starting amount may grow or decline as interest compounds, with no additional deposits or withdrawals.

Results are educational estimates based on the assumptions you enter, not a current rate, recommendation, financial advice, or guarantee of future returns.

Compound interest details

The starting values are an educational example. Enter a rate for the scenario you want to explore.

Basic inputs
From $0 to $1 billion. Example: $10,000.
Enter a nominal rate above -100% and no more than 100%. The 6% default is an illustration; this is not a current or recommended rate.
Use a total duration from 1 month to 100 years.
Compounding frequency
Time to a target
Estimate the first whole month at or above this amount, up to 100 years. Uses your principal, rate, and frequency, independently of the duration above.
Inflation assumption
Purchasing power
Use 0%–25%. The 3% default is an illustration, not a current estimate or forecast.

Balance and cumulative interest

Enter valid assumptions to see the modeled balance and cumulative interest at each year and at the final partial period.

The annual balance table following this chart provides the same data.
Annual balance table
Annual opening balance, interest for the period, and ending balance
Period endingOpening balanceInterestEnding balanceCumulative interest
Enter valid assumptions to generate the schedule.

Values are rounded for display. The CSV export retains raw calculation precision.

Practical guide to compound interest

This calculator answers a focused question: how can one starting amount change when each period's interest becomes part of the balance used for later interest? It is useful for exploring a savings balance, certificate, debt-like growth, or a hypothetical negative-rate scenario when there are no later cash flows.

How to use the calculator

  1. Enter the principal available at the start.
  2. Enter a nominal annual rate for your educational scenario. Do not treat the example rate as a current offer or recommendation.
  3. Choose whole years, optional additional months, and how often interest compounds.
  4. Compare the ending balance with total interest, growth, annual percentage yield (APY), and doubling time.
  5. Use the chart and annual table to inspect the path rather than relying only on the final value.

What the results mean

Ending balance is principal plus modeled interest. Interest earned or lost is the ending balance minus principal. Total growth expresses that change relative to principal. APY converts the selected nominal rate and frequency to a one-year effective yield. Doubling time is the exact modeled time for a positive rate to turn one unit into two under the selected frequency.

Exact formula used

For complete periods, the standard compound-interest formula is:

A = P × (1 + r / m)m × t

Here, P is principal, r is the nominal annual rate as a decimal, m is compounding periods per year, and t is time in years. Because entered months do not always complete a compounding period, the implementation uses:

q = floor(months × m / 12)
f = (months × m mod 12) / 12
A = P × (1 + r / m)q × (1 + (r / m) × f)

The APY is (1 + r / m)m - 1. Positive-rate doubling time is ln(2) / (m × ln(1 + r / m)).

The ending balance in today’s dollars is A / (1 + i)t, where i is your annual inflation assumption and t includes any additional months. Comparison balances and the desired target use nominal dollars.

Worked example

Illustrative assumptions: $10,000 principal, 5% nominal annual rate, 10 years, compounded monthly, with no deposits or withdrawals. The 5% rate is solely an example, not a current rate or recommendation.

A = 10,000 × (1 + 0.05 / 12)120 = $16,470.09

The modeled interest is $6,470.09, total growth is 64.70%, APY is 5.12%, and exact modeled doubling time is about 13.89 years.

Assumptions and limitations

  • There are no contributions, withdrawals, fees, taxes, or rate changes. Only the “In today’s dollars” estimate adjusts for your inflation assumption.
  • The entered rate is nominal and remains constant for the entire model.
  • Whole periods compound. Any final fraction of one compounding period receives prorated simple interest; it does not receive a full period's interest.
  • Daily compounding uses 365 equal periods per year. Real products may use different day counts, accrual rules, rounding, or posting dates.
  • Negative rates model loss but cannot be -100% or lower. Doubling time is not shown for zero or negative rates.
  • Calculations retain floating-point precision internally and round only for display.

For broader conventions, see the calculation methodology. For recurring deposits, withdrawals, fees, taxes, or inflation, use the investment returns calculator.

Frequently asked questions

What is the difference between a nominal rate and APY?

The nominal rate is the entered annual rate before within-year compounding. APY includes that compounding, so a positive nominal rate compounded more than annually generally has a slightly higher APY.

Does this calculator include monthly deposits?

No. It intentionally models one starting principal with no later deposits or withdrawals. Use the investment returns calculator for recurring cash flows.

Why does compounding frequency affect the result?

More frequent compounding moves earned interest into the interest-bearing balance sooner. The difference depends on the nominal rate and duration.

How are extra months handled?

The calculator applies all complete compounding periods first, then prorates simple interest for any fraction of the final period. The ending partial period appears in the chart and table.

Can I enter a negative interest rate?

Yes, for educational comparisons, provided the nominal annual rate is above -100%. The modeled balance declines and no doubling time is shown.

Are taxes, fees, and inflation included?

The “In today’s dollars” estimate adjusts the ending balance for your inflation assumption. Taxes and fees are excluded; use the investment returns calculator to model them.

Glossary

Principal
The amount present at the beginning of the model.
Compound interest
Interest calculated on principal and previously added interest.
Nominal annual rate
An annual rate that does not itself account for within-year compounding.
APY
Annual percentage yield, the effective one-year rate after compounding frequency is included.
Compounding period
The interval at which modeled interest is added to the balance.

Investment returns

Include contributions, withdrawals, fees, inflation, and multiple return assumptions.

Model investment returns