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CALCPARK

Compound Interest Calculator

See how savings grow with daily, monthly, quarterly, yearly or continuous compounding, optional regular deposits, and a year-by-year table of interest earned.

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How to use it

  1. Enter the starting amount, the yearly interest rate and how many years the money stays invested (decimals such as 2.5 are fine).
  2. Pick the compounding schedule your account uses – savings accounts are usually daily or monthly, bonds yearly or half-yearly.
  3. Optionally add a regular contribution every month or year and choose whether it is paid at the start or the end of each period.
  4. Read the final balance, the split between what you deposited and the interest earned, and the APY.
  5. Open the growth table or download it as CSV to see each year’s interest; copy the link to keep the scenario.

Example

10,000 at 5% compounded monthly for 10 years: the monthly rate is 0.05 ÷ 12 = 0.0041667 and there are 120 periods, so the balance is 10,000 × 1.0041667¹²⁰ = 16,470.09. Adding 100 at the end of every month contributes 12,000 and grows to 100 × (1.0041667¹²⁰ − 1) ÷ 0.0041667 = 15,528.23, giving a total of 31,998.32. Of that, 22,000 was deposited and 9,998.32 is interest. The effective annual rate is 1.0041667¹² − 1 = 5.116%.

Formulas and assumptions

Lump sum:       A = P · (1 + r/n)^(n·t)        continuous: A = P · e^(r·t)
Contributions:  FV = PMT · ((1 + i)^N − 1) / i     × (1 + i) if paid at the start of each period
                i = (1 + r/n)^(n/m) − 1   (rate per contribution period, m payments a year), N = m · t
Interest earned = A + FV − P − PMT · N
APY = (1 + r/n)^n − 1

P is the starting amount, r the nominal yearly rate, n the number of compounding periods per year (365, 12, 4 or 1), t the time in years, PMT the contribution and m how many contributions are made per year. When the contribution schedule differs from the compounding schedule – for example monthly deposits into a daily-compounding account – the rate per contribution period is derived from the compounding factor, so interest between deposits is credited correctly. The growth table evaluates the same formulas at each year end; a fractional final year is pro-rated in the last row.

Assumptions and limits: the rate stays fixed for the whole term, contributions are constant, no withdrawals, fees or taxes are deducted, and daily compounding uses 365 periods a year (banks sometimes use 360 or 365/366). Amounts are shown with two decimals but calculated at full precision.

Sources: US Securities and Exchange Commission – Compound interest, Consumer Financial Protection Bureau – APY.

Projections only. Real accounts have variable rates, fees and taxes; this is not investment advice.

Questions

Should I enter the APR or the APY?
Enter the nominal yearly rate (APR) together with the compounding schedule; the calculator then shows the APY. If your bank only quotes an APY, choose yearly compounding and enter the APY as the rate – the result is the same.
What is the difference between start-of-period and end-of-period contributions?
A start-of-period deposit earns interest for one extra period. Over 10 years of 100-a-month deposits at 6% that is 16,469.87 instead of 16,387.93 – a difference of one month of growth on the whole stream.
Why is daily compounding barely better than monthly?
The gain from more frequent compounding shrinks quickly and converges to the continuous limit e^(rt). At 5% over 10 years, daily beats monthly by only 16.56 on 10,000, and continuous compounding adds just 0.56 more.