semkuCompound interest calculator
Enter the principal, rate of return and period to see the expected result for a lump sum and for monthly contributions, shown separately.
Change calculation settings
Enter amounts like 1,000 and rates like 5.5.
Sources
U.S. Securities and Exchange Commission, Investor.gov — Compound Interest (glossary)
This glossary entry defines compound interest as interest paid on principal and accumulated interest; regular contributions, deferral, contribution timing and rounding follow the model below.
University of Washington, Math 111 — formula handouts
The handout gives the future value of an ordinary annuity, R((1+i)^n−1)/i, and the extra (1+i) factor for an annuity due; withdrawals use the same formula with a negative payment, added to the growth of the initial balance.
Compound interest rules in detail
For a lump sum, the same rate is applied to the previous principal and accumulated return at every compounding interval. If you choose an annual rate of 12% compounded monthly, it is treated as a nominal annual rate and 1% is applied 12 times. This differs from an effective annual rate of 12%.
Monthly contributions are supported only with monthly compounding. End-of-month contributions are added after each month’s return is calculated; start-of-month contributions are added before it. During a deferral only the initial principal compounds, and monthly contributions start when the deferral ends. The initial deposit is treated as paid in at the start of the first month and compounds at the same monthly rate throughout the calculation period, including any deferral. P is initial principal, a the nominal annual percentage rate, m the yearly compounding count and n the total lump-sum compounding count; for monthly contributions m=12, N is total months including deferral, d is deferred months, k=N−d is the contribution count, C is the monthly contribution and τ is 0 for month-end or 1 for month-start. i = a/(100m); FV = P(1+i)^n; FVₘ = P(1+i)^N + C × S × (1+i)^τ; S = ((1+i)^k−1)/i (i≠0), S=k (i=0); APY = 100×((1+i)^m−1)%.
If the rate is 0%, the principal and contributions are simply added without the division formula. Fractional periods, daily compounding and a remaining period that does not match the compounding interval are not estimated or interpolated. All amounts are before tax and do not account for fees or inflation.
Keep internal precision and round monetary amounts once to cents for final display, with halfway values rounded away from zero. Because each amount is rounded separately, the sum of the displayed amounts may differ from the displayed total by one cent.
If you choose Withdrawal, the monthly amount is taken out of the balance instead of paid in: it enters the same formula as a negative C, with the same month-end or month-start timing and deferral. If the balance would fall below $0 during the period, no final amount is shown; the result names the month in which that happens.
Frequently asked questions
- How is monthly compounding calculated?
- If you enter an annual rate of 12% as a nominal rate and choose monthly compounding, 1% is applied each month. After 12 months the effective annual rate is about 12.68%. This is different from dividing an
effective 12% annual rateby 12. - Do monthly contributions compound too?
- Contributing every month is a way of paying in; compounding means the return earned on each contribution is included in the next calculation. semku shows the initial principal, the contributions and the expected return separately.
- Can I let a lump sum grow for a while before I start contributing monthly?
- Enter the number of months in
Deferral before contributions. During the deferral only the initial principal is calculated, and monthly contributions are applied at the chosen timing from the month after the deferral ends. - Can I compound 1% per day?
- Daily compounding is not supported at the moment. A high short-term rate repeated over a long period does not represent a real return, and the rate you enter is not a guaranteed value.
- Can I calculate contributions that differ from month to month?
- The contributions tab currently supports only the same amount every month. Entering an arbitrary average of differing monthly amounts gives a different result, so it is not presented as a supported calculation.
Privacy on this page
Calculations run in your browser. The principal, rate, period and contribution amounts you enter are not sent to the server or saved in browser storage. Reloading the page returns the inputs to their initial state.
To understand how the page is used and to improve the service, this page sends semku’s own usage statistics and automatic error reports. They go only to the dedicated endpoint under semku.com/api/telemetry/v1/. They are not used for advertising or third-party tracking.
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Operations and sessions are distinguished by randomly generated identifiers. In the browser, these identifiers exist only in temporary memory and are not written to cookies or browser storage. No identification based on cookies or combined device characteristics is used.
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For details, see the privacy policy.
Calculations run in your browser without sending the financial values you enter to the server or storing them. Results are pre-tax estimates based on the assumptions you enter; they do not guarantee or account for actual returns, taxes, fees or inflation.