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

How to Use the Calculator

1. Enter your initial deposit and annual rate (APR).
2. Choose compounding frequency and the time in years.
3. (Optional) Add a recurring contribution, its frequency, and timing (begin or end).
4. (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.

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

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.

… (Formulas as above; preserved & harmonized) …

','\

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

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

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}

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

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

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