Compound Interest Rate Calculator

Plan faster with a transparent compound interest calculator that handles contributions fees taxes inflation and flexible compounding. Compare scenarios in seconds. See growth charts schedules and effective annual rate. Export CSV or PDF. Save and share results for confident decisions. Includes goal seek real value outputs mobile friendly design accessible controls and detailed explanations

Inputs

Currency symbol

Start date (optional)

Initial principal

One-time fee (flat)

Nominal APR (%)

Compounding

Years

Months

Periodic contribution

Contribution timing

Annual fee (% of balance)

Tax rate on interest (%)

Inflation (annual %)

Goal Seek Ignores fees taxes inflation

Target future value

Contribution frequency equals compounding frequency. For continuous compounding contributions are treated as if compounded at the nominal rate each period.

Formula & Assumptions

We simulate period by period using the chosen compounding frequency. Each period we optionally add contribution, accrue interest, then subtract fees and taxes on interest. For continuous compounding we approximate with high-frequency discrete steps.

Show math

Nominal rate r (decimal). Frequency n. Periodic rate i = r/n (continuous: i ≈ r/12 at high frequency). If timing is end-of-period:

B_{t+1} = (B_t + C) * (1 + i) - fee - tax

Beginning-of-period uses B_t + C before interest. Annual fee % is spread as fee = B_{t+1} * (feeAnnual/n). Tax is max(interest,0) * taxRate. Real value divides the final balance by (1 + inflation)^{years+months/12}.

Final value

Total contributions

Total interest

Fees paid

Taxes paid

Real value

Amortization Schedule

#	Date	Contribution	Interest	Fees	Taxes	Balance

Understanding the Calculator & Formulas

This compound interest calculator models real‑world saving and investing with clear, auditable math. It accepts a starting principal, a nominal annual percentage rate (APR), a compounding frequency, and an optional periodic contribution. You can adjust contribution timing (beginning or end of period), add an annual percentage fee, include a one‑time setup fee, apply taxes on interest, and optionally account for inflation to show results in today’s purchasing power. Outputs include headline KPIs, a growth chart, and a detailed period‑by‑period schedule so you can verify how each number is produced.

The engine simulates each compounding period. If contributions occur at the beginning of a period (an “annuity‑due”), they are added before interest; otherwise, contributions are added after interest as an “ordinary annuity.” Fees are assessed as a proportion of balance each period, and taxes are applied to positive interest earned that period. With daily compounding you can choose a day‑count basis (Actual/365‑approx or Actual/360‑approx) to mirror bank conventions. Selecting continuous compounding uses an exponential approximation which closely matches very‑high‑frequency compounding for planning purposes.

Core Formulas

Let P_0 be the initial principal, r the nominal APR (decimal), n the compounding periods per year, and i = r/n the periodic rate. Over m periods, the future value without contributions is FV = P_0(1+i)^m. With a fixed contribution C each period:

End‑of‑period (ordinary annuity): FV = P_0(1+i)^m + C\left((1+i)^m - 1\right)/i.

Beginning‑of‑period (annuity‑due): multiply the contribution term above by (1+i).

The effective annual rate (EAR, often called APY) translates nominal APR and compounding into a single comparable figure: EAR = (1 + r/n)^n - 1; for continuous compounding, EAR = e^{r} - 1. Inflation‑adjusted (real) value divides the nominal future value by (1+\pi)^{t}, where \pi is annual inflation and t is years. In this tool, fees and taxes are applied per period during simulation; exact closed‑forms for those frictions are messy, so a transparent step‑by‑step ledger is preferred.

Key symbols and where they appear
Symbol	Meaning	Used in
`P_0`	Initial principal	Base growth
`r`	Nominal APR (decimal)	Rates & EAR
`n`	Compounds/year	Periodic rate, EAR
`i`	Periodic rate `= r/n`	All formulas
`C`	Periodic contribution	Annuity term
`m`	Total periods	Exponent & annuity
`\pi`	Annual inflation	Real value

EAR examples at 7% nominal
Frequency	Periods	EAR
Annual	1	7.000%
Semiannual	2	7.122%
Quarterly	4	7.186%
Monthly	12	7.229%
Daily (365)	365	7.251%
Continuous	∞	7.251%

Goal Seek & Verification

The goal‑seek feature solves for the required periodic contribution to reach a target future value, ignoring fees, taxes, and inflation to keep the algebra clean. Rearranging the ordinary‑annuity equation: C = \dfrac{FV - P_0(1+i)^m}{\left((1+i)^m - 1\right)/i}, and multiply by (1+i) for annuity‑due timing. After solving, the simulator re‑runs the full ledger so you can inspect the impact of fees or taxes under your real assumptions.

Finally, note the difference between nominal and real growth. A portfolio growing 7% nominal with 3% inflation has a real growth rate roughly (1.07/1.03 − 1) ≈ 3.88%. The “Real value” KPI in the tool computes this properly over your exact horizon and helps compare outcomes across inflation scenarios.

This content is educational and does not constitute financial advice. Always validate results against your institution’s statements and consult a qualified professional for tax or investment guidance.