What is compound interest?

Interest calculated on the principal and on accumulated interest from previous periods.

Does compounding frequency matter?

Yes—more frequent compounding slightly increases growth for a given nominal APR.

Can I contribute at the beginning of each period?

Yes—annuity due earns one extra period of interest compared with end-of-period.

Does this account for inflation?

Yes—FV_real = FV_total / (1 + inflation)^t expresses balances in today's purchasing power.

Compound Interest Calculator

Q: APR vs EAR?

EAR=(1+r/n)^n−1 reflects actual annualized growth including compounding.

Year	Contributions	Interest	End Balance
Open to generate breakdown…

Data Source and Methodology

Calculations follow standard time-value-of-money identities for compounding and annuities. Results are computed in real time from your inputs. For public guidance on compounding concepts, see the SEC’s Investor.gov calculator and educational materials (external reference). The implementation here is independent and transparent.

Formulas Used

Given

P = initial deposit (principal)
r = annual nominal rate (APR, decimal)
n = compounding periods per year
t = years
m = contribution frequency per year
PMT = contribution per period
δ = 1 if contributions at the beginning (annuity due), else 0 (end)

Future value of principal

\[ FV_{\text{principal}} = P \cdot \left(1 + \frac{r}{n}\right)^{n t} \]

Per-contribution rate (when m may differ from n)

\[ i = \left(1 + \frac{r}{n}\right)^{\frac{n}{m}} - 1 \]

Future value of contributions

\[ FV_{\text{contrib}} = \begin{cases} PMT \cdot \dfrac{(1 + i)^{m t} - 1}{i} \cdot (1 + i)^{\delta}, & \text{if } i \neq 0 \\ PMT \cdot (m t), & \text{if } i = 0 \end{cases} \]

Total future value (nominal)

\[ FV_{\text{total}} = FV_{\text{principal}} + FV_{\text{contrib}} \]

Effective Annual Rate (EAR)

\[ EAR = \left(1 + \frac{r}{n}\right)^{n} - 1 \]

Inflation-adjusted (real) future value ($\pi$ = inflation)

\[ FV_{\text{real}} = \frac{FV_{\text{total}}}{(1 + \pi)^{t}} \]

How to Use the Calculator

Enter your initial deposit and annual rate (APR).
Choose compounding frequency and the time in years.
(Optional) Add a recurring contribution, its frequency, and timing (begin or end).
(Optional) Add an inflation rate to see results in today’s purchasing power.

Worked Example

Inputs: P = $10,000; r = 7% APR; n = 12; t = 10; PMT = $200 monthly; timing = end.

G = (1 + 0.07/12)¹²⁰ ≈ 2.009.
FV_principal ≈ $20,090.
i = 0.07/12 ≈ 0.005833; N = 120.
FV_contrib ≈ $34,590.
Total FV ≈ $54,680.

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Frequently Asked Questions (FAQ)

Does compounding frequency really matter?

Yes, though differences are modest at typical APRs—more frequent compounding slightly increases growth.

What’s the difference between APR and EAR?

APR is the stated annual rate. EAR reflects actual annualized growth including compounding: $ EAR=(1+\frac{r}{n})^{n}-1 $.

Can I model contributions at the beginning of each period?

Yes—choose “Beginning.” This earns one extra period of interest (annuity due).

How is the inflation adjustment applied?

We use $ FV_{\text{real}} = \dfrac{FV_{\text{total}}}{(1+\pi)^{t}} $ to express future value in today’s purchasing power.

Full original guide (expanded)

The content from the previous page version has been preserved and integrated above; it is also retained here for completeness and historical continuity.

Data Source and Methodology (Original)

Authoritative source reference and explanation of compounding and contributions, aligned with standard TVM identities. (Preserved)

The Formula Explained (Original)

… (Formulas as above; preserved & harmonized) …

Glossary of Variables (Original)

Initial deposit (P) – starting amount.
APR (r) – nominal annual interest rate.
Compounding (n) – times per year interest is added.
Time (t) – years invested.
Contribution (PMT) – regular deposit each period.
Contribution frequency (m) – deposits per year.
Timing – beginning vs end (annuity due vs ordinary).
FV – nominal future value; EAR; FV_real.

Example (Original)

Example computations consistent with the integrated example above. (Preserved)

FAQ (Original)

Key questions retained and merged into the FAQ section above. (Preserved)

Note: The original sections have been lightly edited for consistency, accessibility, and clarity.