Compound Interest Calculator

Data Source and Methodology

Authoritative source: U.S. Securities and Exchange Commission (SEC) — Investor.gov, “Compound Interest Calculator,” last updated 2024, available at investor.gov. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

This tool applies standard time-value-of-money identities for compounding and annuities, using the effective per-period rate implied by your compounding frequency and contribution cadence.

The Formula Explained

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

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

Effective rate per contribution period (when m may differ from n):
$$
i_c = \left(1 + \frac{r}{n}\right)^{\frac{n}{m}} - 1
$$

Future value of contributions:
$$
FV_{\text{contrib}} =
\begin{cases}
PMT \cdot \dfrac{(1 + i_c)^{m t} - 1}{i_c} \cdot (1 + i_c)^{\delta}, & \text{if } i_c \neq 0 \\
PMT \cdot (m t), & \text{if } i_c = 0
\end{cases}
$$

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 using annual inflation π:
$$
FV_{\text{real}} = \frac{FV_{\text{total}}}{(1 + \pi)^{t}}
$$

Glossary of Variables

• Initial deposit (P): Starting amount invested today.
• APR (r): Nominal annual interest rate, expressed as a percentage.
• Compounding (n): How many times per year interest is added to the balance.
• Time (t): Investment duration in years (decimals allowed).
• Contribution (PMT): Regular amount added each contribution period.
• Contribution frequency (m): How often contributions are made per year (e.g., 12 for monthly).
• Timing: Beginning or end of period (annuity due vs. ordinary annuity).
• Future Value (FV): Ending balance before inflation adjustment.
• EAR: Effective Annual Rate implied by APR and compounding.
• Inflation-adjusted FV: Future value expressed in today’s purchasing power.

Come Funziona: Un Esempio Passo-Passo

Inputs: P = $10,000; r = 7% APR; n = 12 (monthly); t = 10 years; PMT = $200 per month; timing = end of period.

1. Compute growth factor: G = (1 + r/n)^(n·t) = (1 + 0.07/12)^(120) ≈ 2.009.
2. Principal future value: FV_principal ≈ 10,000 × 2.009 ≈ $20,090.
3. Monthly rate i = r/n ≈ 0.005833; number of contributions N = 12 × 10 = 120.
4. FV of contributions (end): FV_contrib ≈ 200 × [((1 + i)^N − 1)/i] ≈ 200 × 172.95 ≈ $34,590.
5. Total FV ≈ $20,090 + $34,590 ≈ $54,680.

Contributions total $34,000 ($10,000 initial + $24,000 recurring), so interest earned is roughly $20,680 before inflation.

Frequently Asked Questions (FAQ)