How to use this compound interest calculator
Enter the initial principal, nominal annual percentage rate, and a whole-year duration from zero to one hundred. Choose annual, quarterly, monthly, or daily compounding. Enter the deposit per selected period: a monthly frequency uses a monthly deposit, while an annual frequency uses an annual deposit. Choose beginning or end of period, then review total contributed, interest, ending balance, and the yearly breakdown. Changing the frequency also changes how often the stated deposit occurs, so adjust its amount when comparing the same annual savings budget.
How the calculation works
Compounding means credited interest becomes part of the balance used in subsequent interest calculations. With no new deposits, the ending amount is P × (1 + r/n)^(nt), where r is the nominal annual decimal rate and n is the number of compounding periods per year. The effective annual rate is (1 + r/n)^n − 1. Neither rate is a historical performance measure or a promise that a financial product will earn the assumed return.
Equal end-of-period deposits form an ordinary annuity. Their future value is C × [(1 + i)^N − 1]/i, with i equal to the periodic rate and N the total periods. Beginning-of-period deposits receive one additional period of growth, so their future value is multiplied by 1 + i. The original principal starts at time zero in both cases. At a zero rate, there is no division by zero: deposits simply sum to C × N.
Deposit timing and frequency must match the scenario. Depositing 100 every month for one year adds 1,200, whereas depositing 100 every quarter adds only 400. A comparison that keeps the per-period deposit unchanged while changing frequency changes both the interest model and the savings budget. If you want to isolate frequency, set deposits to zero or adjust the deposit amounts so total contributed is comparable. Irregular deposits and withdrawals require a separate cash-flow model.
The rate is nominal before compounding. A quoted APY or effective annual yield already incorporates compounding and should not be substituted directly into the nominal field. Daily mode uses 365 periods in every model year, with one deposit every model day if deposits are enabled. It does not apply actual dated transactions, leap-year accrual, varying rates, business-day posting, tax, fees, inflation, or market volatility. The yearly table follows these same assumptions throughout the selected horizon.
Formulas
Periodic rate and periods
Ending balance with end-of-period deposits
Contribution timing and interest
Worked examples
One lump sum
Starting with 10,000 at a nominal 5%, monthly compounding, and five years gives 60 periods at 0.05/12. With no additional deposits, the projected ending balance is approximately 12,833.59, of which approximately 2,833.59 is interest. Principal remains 10,000, so the increase can be checked directly by subtraction.
Regular deposits without interest
With an initial 1,000, a zero rate, deposits of 100 each month, and two years, total added deposits are 100 × 24 = 2,400. The ending balance is 3,400 and earned interest is zero. A larger ending amount is not necessarily investment growth; this example's entire increase comes from contributions.
Beginning versus end of year
With no initial principal, a 10% rate, annual compounding, and a 100 annual deposit for two years, end-of-year deposits produce 210: the first 100 grows once and the second arrives at the end. Beginning-of-year deposits produce 231 because each deposit receives one additional year of growth. Both cases contribute the same 200.
Common uses
Plan a regular contribution illustration
Specify an initial balance and the same deposit every period to see contributed money separately from modeled interest. Compare the annual table with your savings budget. If deposits are monthly, keep monthly compounding selected for this version; other timing combinations require a model that handles those separate schedules.
Compare contribution timing
Hold the number and size of deposits constant while switching between beginning and end of period. The earlier deposits receive more time to grow. This demonstrates a timing effect without assuming that a real account credits deposits immediately or allows every planned payment on the stated date.
Distinguish deposits from returns
Review the contribution total before interpreting an increase in balance. A balance can grow significantly because money was added even when interest is small or zero. Keeping contributions and interest separate avoids treating an entire account increase as investment profit, particularly when comparing scenarios with different deposit frequencies.
Accuracy and limitations
The future-value formula combines initial principal with a level annuity and handles zero rates explicitly. Whole-year terms provide complete annual, quarterly, monthly, or 365-day model periods. Beginning-of-period timing changes growth duration but does not add a deposit. The yearly table follows the identical formula at each year boundary.
Constant-rate growth is a deterministic illustration, not a return forecast. Deposits must be nonnegative and uniform. Actual calendar days, withdrawals, charges, taxes, inflation, interest-rate changes, and market losses are excluded. Results beyond the supported numerical range are rejected with a visible message.
Sources and methodology
These references support the formulas and financial concepts explained on this page. Product-specific rates, fees, and contract conventions still need to be checked with the provider.
Frequently asked questions
Are deposits always monthly?
No. They occur once per chosen compounding period. Read the dynamic deposit label and adjust the amount if you change frequency.
What is included in total contributed?
Initial principal plus all scheduled deposits. Interest earned is the ending balance minus that contribution total.
Does beginning-of-period timing add an extra deposit?
No. The number of deposits stays the same, but each one receives one additional period of growth.
Can I enter withdrawals or irregular contributions?
This version accepts nonnegative equal deposits only. Withdrawals, dated transactions, and varying contributions need a separate cash-flow calculation.
Is the effective annual rate the account's APY?
It is the effective annual result of this mathematical nominal-rate model. An actual disclosed APY can follow specific product and regulatory rules.
Is a projected investment balance guaranteed?
No. Constant-rate compounding is an illustration. Investments can lose value and actual returns, charges, taxes, and inflation can change the outcome.