Visual Compound Interest & Contribution Growth Curve
Compound interest grows capital exponentially according to $FV = P(1+r)^n + PMT\frac{(1+r)^n - 1}{r}$, generating 'interest on interest' that eventually surpasses cumulative out-of-pocket contributions.
FV = P(1 + r)^n + PMT × [(1 + r)^n − 1] / rInputs & Parameters (4)
20-Row Comparison Table
| # | Initial Principal (P) ($) | Future Portfolio Value (FV) | Total Contributions | Compound Growth |
|---|---|---|---|---|
| 01 | 0 $ | $475,513 | $150,000 | $325,513 |
| 02 | 13,000 $ | $570,935 | $163,000 | $407,935 |
| 03 | 26,000 $ | $666,358 | $176,000 | $490,358 |
| 04 | 39,000 $ | $761,780 | $189,000 | $572,780 |
| 05 | 53,000 $ | $864,543 | $203,000 | $661,543 |
| 06 | 66,000 $ | $959,965 | $216,000 | $743,965 |
| 07 | 79,000 $ | $1,055,387 | $229,000 | $826,387 |
| 08 | 92,000 $ | $1,150,809 | $242,000 | $908,809 |
| 09 | 105,000 $ | $1,246,232 | $255,000 | $991,232 |
| 10 | 118,000 $ | $1,341,654 | $268,000 | $1,073,654 |
| 11 | 132,000 $ | $1,444,416 | $282,000 | $1,162,416 |
| 12 | 145,000 $ | $1,539,839 | $295,000 | $1,244,839 |
| 13 | 158,000 $ | $1,635,261 | $308,000 | $1,327,261 |
| 14 | 171,000 $ | $1,730,683 | $321,000 | $1,409,683 |
| 15 | 184,000 $ | $1,826,106 | $334,000 | $1,492,106 |
| 16 | 197,000 $ | $1,921,528 | $347,000 | $1,574,528 |
| 17 | 211,000 $ | $2,024,290 | $361,000 | $1,663,290 |
| 18 | 224,000 $ | $2,119,713 | $374,000 | $1,745,713 |
| 19 | 237,000 $ | $2,215,135 | $387,000 | $1,828,135 |
| 20 | 250,000 $ | $2,310,557 | $400,000 | $1,910,557 |
Key Analytical Takeaways
- 01The Compounding Crossover Point marks the year when cumulative investment gains exceed total out-of-pocket cash contributed.
- 02By rule of 72 ($T_{2\times} \approx 72 / r$), an 8% annual return doubles invested capital roughly every 9 years without counting fresh contributions.
- 03Time in the market dominates contribution size: the final 10 years of a 30-year curve generate more dollar growth than the first 20 years combined.
Frequently Asked Questions
What is the difference between simple interest and compound interest?+
Simple interest pays a fixed return only on the initial principal, creating a straight line. Compound interest reinvests each period's earnings so future returns are calculated on a continually expanding base.
How does monthly compounding compare to annual compounding?+
Monthly compounding applies 1/12th of the nominal rate each month, producing an Effective Annual Yield (APY) of (1 + r/12)^12 - 1, which is slightly higher than the nominal rate.
What is the Rule of 72 in compound growth?+
Dividing 72 by your annual percentage return estimates how many years it takes an untouched lump sum to double—for example, at 8% annual return, capital doubles every ~9 years.