This website focuses on select topics in financial algebra, financial calculus, numerical methods, derivatives pricing and related computations.

## Algebra

The algebra section covers topics like the calculation of annuities and compound interest including mathematical derivations of some important formulas. For instance, it shows how compound interest converges to an exponential function as compounding intervals become infinitesimally small.

\lim_{m \to \infty}(1 + \frac{r}{m})^{m \cdot \tau}= exp(r \cdot \tau)

## Optimize Porfolios Calculating Logarithmic Returns

Learn how to manage investment risks and optimize the proportion of risky positions in portfolios by calculating logarithmic returns. Simply by reducing the size of risky positions, the overall investment performance can swing from the negative into the positive.

## Monte Carlo Simulation of Returns

Monte Carlo Simulation is a superior way of assessing risks pricing complex derivatives. Learn about its principles and the difference between expected value and expected return.

## Interest Rate Calculators

The interest calculator section of this blog provides calculator forms for various compound interest applications. The calculators perform valuations, assess investment returns, and compute parameters for financial contracts. Moreover, they are useful for educational purposes since each calculator page includes explanations on the underlying mathematics and financial economics.

For example, the return on investment calculator page explains why we assume exponential growth in order to compute an annualized return on investment.