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Tool 6

Investment calculators · Timing made explicit

Compound Interest Calculator

Created by Arunangshu DasReviewed

Explore a lump sum or recurring savings plan. Separate your contributions from interest, choose deposit timing and inspect effective annual growth from a nominal rate.

Fixed-rate, matched-period hypothetical projections. No forecast, bank-statement guarantee, tax calculation or personalized investment advice.

Preparing calculator…

Savings assumptions and actions

Make the timing explicit

Recurring deposits use the same interval as compounding. This model uses a fixed nominal annual rate and complete years. It does not predict market returns or reproduce a bank statement.

Formatting only. No FX conversion or tax adjustment.

Money already present at time zero, separate from recurring deposits. Enter 0 explicitly if none.

Changing frequency clears the recurring deposit to prevent silently changing the savings commitment. Daily means 365 equal periods each year, including leap years.

One nonnegative deposit each selected period. Enter 0 for a lump sum only. Withdrawals are outside this model.

Beginning deposits receive one extra period of growth or loss. At zero years, neither timing adds any deposit.

Greater than −100% through 1000%. Do not enter an effective APY/AER as a nominal rate; compounding is applied separately.

Whole years only; no fractional-year or actual-date accrual. No per-period cent rounding.

Projected balance

Enter all four numeric assumptions, or load the independently verified example.

80 significant decimal digits internally; half-even display rounding. Currency rounds to 2 places; a nonzero amount below one cent is marked. Inputs stay in browser memory.

Know which money came from you

A projected balance includes your starting principal and every later deposit. Only the difference from total contributed capital is interest earned or lost.

Read the complete compound interest guide

Formula and methodology

q = 1 + R/(100m); N = mY
End: FV = Pq^N + CΣ(k=0…N−1)q^k
Beginning: FV = Pq^N + CqΣ(k=0…N−1)q^k
Interest = FV − (P + CN)

Let P be principal, C the deposit per period, R the nominal annual percentage, m periods per year, Y complete years, N=mY, and q=1+R/(100m). End-period balance is Pq^N+C times the sum of q^k for k=0 through N−1. Beginning timing multiplies only that deposit term by q. The engine uses stable binary composition of growth and geometric sums, not subtraction of nearly equal powers or division by a tiny rate.

At zero interest, balance is P+CN. At zero years it is P, with no recurring deposit. Effective annual growth is (q^m−1)×100. Stable accumulation and an isolated 80-digit decimal context protect small-rate arithmetic; rounding occurs only for display.

Verified worked example

Start with 1,000, add 100 at the end of each year for two years at a nominal 5% compounded annually. Year one: 1,000×1.05+100=1,150. Year two: 1,150×1.05+100=1,307.50. Of this, 1,200 is contributed capital and 107.50 is interest. Beginning-year deposits instead produce 1,317.75, with the same contributed capital.

Inputs and interpretation

Choose the display currency and matched compounding/deposit interval. Enter initial principal, recurring deposit per selected interval (explicit 0 if none), deposit timing, nominal annual rate and complete years. Re-enter the deposit after a frequency change. Compare contributed capital, interest and the optional selected-year milestones; use Clear values to reset.

Assumptions and limitations

Constant nominal rate; equal nonnegative deposits; matching deposit and compounding frequencies; complete integer years; initial principal separate from deposits. Daily means 365 equal periods every year, not calendar accrual. Growth is reinvested, with no contractual period-by-period cent rounding.

Supported domain and common mistakes

No withdrawals, variable rates, continuous compounding, fractional years, independently scheduled deposits, actual-date accrual, taxes, fees, inflation or FX. Currency is formatting only. Each amount is at most 10^15; rate greater than −100% through 1000%; years 0–100; projected balance at most 10^30. Decimal input uses a point, up to 12 fractional places and 48 characters. Unsupported results are refused, not clipped.

Entering an effective APY/AER as a nominal rate can apply compounding twice. Treating the entire projected balance as investment earnings counts your own deposits as profit. Changing a monthly deposit into a daily deposit without changing its amount radically changes contributions. A higher projection does not establish a better or safer investment.

Frequently asked questions

Can I add monthly deposits?
Yes. Select Monthly and enter the amount added each month. Deposits and compounding share one interval in this model. An annual-compounding account with independently timed monthly deposits is outside this model; do not treat it as an exact bank statement.
Why is my recurring deposit cleared when I change frequency?
The amount is per selected interval. Keeping 100 while switching from annual to daily would change two years of deposits from 200 to 73,000. Clearing the field asks you to confirm the new commitment instead of silently changing it.
Should I enter a nominal rate or an effective APY/AER?
Enter a nominal annual percentage. This tool divides it by the selected periods per year and then compounds. Effective APY/AER already includes compounding under its own assumptions; entering it unchanged as nominal can overstate growth.
What happens with zero years or zero interest?
At zero years the result is just initial principal, with no recurring deposit even under beginning timing. At zero interest, balance equals principal plus deposit times the number of periods. There is no division by zero.
Can interest be negative, and does beginning timing always help?
Rates greater than −100% through 1000% are supported as hypothetical nominal scenarios. Negative rates can produce negative interest. Beginning deposits are exposed for one extra period, which helps with positive rates and can hurt with negative rates.
Does daily compounding count leap days?
No. Daily is a fixed 365-period year, including leap years. This calculator has no actual dates, bank day-count or interest-posting conventions. For an actual account use its contractual accrual rules.
Are taxes, inflation and currency conversion included?
No. The projection is in future money before tax, fees and inflation. USD, GBP, CAD, AUD and INR selection changes display formatting only, and does not convert an amount or apply account-specific allowances.

Sources and educational scope

Hypothetical mathematical projections for education, not personalized financial or investment advice. Rates and future returns are uncertain. Verify actual product terms, cash-flow timing, fees, taxes and inflation before making a decision. No future balance or suitability is promised.

Reviewed . AI-assisted content; operator editorial responsibility. No independent expert financial review is claimed.

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