Compound Interest Calculator

① Lump-Sum Initial Principal Future Value ($FV_{\text{principal}}$):

- $$FV_{\text{principal}} = PV \times \left(1 + \frac{r}{m}\right)^{m \times t}$$

- Where $PV$ is initial principal, $r$ is annual return rate (decimal), $m$ is compounding frequency per year (monthly $m=12$, quarterly $m=4$, annual $m=1$), and $t$ is duration in years.

② Regular Monthly Contribution Future Value ($FV_{\text{annuity}}$):

- For monthly compounding ($m=12$) with monthly interest $i = r / 12$ and total periods $n = t \times 12$:

$$FV_{\text{annuity}} = PMT \times \frac{(1 + i)^n - 1}{i}$$

③ Total Portfolio Value ($FV_{\text{total}}$):

- $$FV_{\text{total}} = FV_{\text{principal}} + FV_{\text{annuity}}$$

④ Effective Annual Rate (EAR):

- Higher compounding frequencies elevate the effective yield above nominal rates:

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

① Mental Math with the Rule of 72 ($T_{\text{double}} \approx \frac{72}{r}$):

- 4% Return: $72 \div 4 = 18$ years to double capital.

- 7% Return: $72 \div 7 \approx 10.3$ years to double capital.

- 10% Return: $72 \div 10 = 7.2$ years to double capital.

- 12% Return: $72 \div 12 = 6.0$ years to double capital.

② Tenet 1: Time in the Market > Timing the Market:

- An investor who invests from age 20 to 30 and stops will often have more total wealth at age 60 than an investor who starts at age 30 and invests three times as much capital for 30 years.

③ Tenet 2: Reinvest All Dividends & Capital Gains (DRIP):

- Withdrawing dividends breaks the exponential compounding curve, collapsing growth into linear returns.

④ Tenet 3: Avoid Catastrophic Drawdowns (Maximum Drawdown / MDD):

- A -50% loss requires a +100% gain just to break even. Broad index fund diversification preserves steady exponential compounding trajectories.