Layered Asset Theory Examining Portfolio Curves: Portfolio Analysis Statistical Regularity Strategy The 5-cent Strategy (Option Strategies) Using Compound Interest to Optimize Investment Spread Advanced Compound Interest: Mathematical Origins & Research Quantitative Investing Strategies: Polynomial Reduction Theory Market Dynamics: Predicting Financial Market Movements Using Quantitative Data Stock Scraping in R: The Comprehensive Step-by-Step Analysis Crypto Fees

# Advanced Compound Interest: Mathematical Origins & Research

Before reading this analysis, it is advised to read the Regular Investing analysis, as it develops the basis behind many of our foundational formulas represented here.

We know that any polynomial can be represented as a finite, descending sum via Polynomial Reduction Theory:

### f (x) = L * Σ { xᵃ(a!) / xⁿ(a-n)! }, where the summation is bounded by {n =0, a}

As an example, let's display f (x) = 3x³ + 12x² + 14 as a finite sum:

### (3x³ + 12x² + 14) / (x³ + x² + 6x + 6) = L

Essentially, we're drawing out the constants of the equation so that only the base values remain, so that when we take a derivative, the base values (the variables) are the only things that change. This makes it extremely easy to do otherwise-impossible calculations in the span of minutes.

Let's simplify L down.

### I = Prᵗ + Mr ᵗ ( r ᵗ-1 ) / ( r -1 )

T will always end up as a constant, no matter how the formula is manipulated. Therefore, the compound interest itself can be viewed as a polynomial: all we need to do is apply PRT to it, so we can find the optimal strategy for our situation.