Introduction Mathematics is an exact fundamental science that allows us to explore the world through a numerical-character alphabet through the study of orders and patterns. It is one of the oldest sciences since, even in primitive communities, the distribution, counting, and division of resources were critical tasks. By now, however, mathematics has become much more complex, extensive, and diverse than it was thousands of years ago, but its overall core, the study of the relationships between objects, has remained unchanged. It is noteworthy that mathematics is not didactically related to the natural sciences, but their existence without the use of mathematical apparatus turns out to be impossible. In other words, many fields of knowledge use mathematical formulas, theorems, and axioms as tools-not surprising at all, given how diverse this science is. Anything from analytic and applied geometry, calculus, differential equations and functional analysis, linear algebra, and even number theories is the subject of mathematics. In this extended essay, in an attempt to narrow the range of mathematical studies to a single topic for the purpose of more in-depth study, the direction of interest calculus, mainly compound interest, has been chosen. A fundamental thesis reflected throughout the paper is that compound interest is a more complex and ambiguous problem than students are used to perceiving it. This extended essay sheds light on the use of interest — in priority of compound interest — to solve many applied problems. The widespread view that compound interest can be helpful only in financial calculations is critically evaluated in the paper: counterarguments are offered to the reader. The essay, however, aims at a deeper study of the compound interest model in the economic sector as well, since it will be shown that the use of mathematical operators, whether limits or differentiation, over the compound interest formula is of applied importance. The didactic benefits of this essay include a broad but critical discussion of the history of compound interest through a literature review of academic and Web sources. It will be shown that compound interest was first used much earlier than is commonly considered. Ultimately, the entire extended essay is a critical assessment of the topic of compound interest and the prospects for its application to life’s problems. Background Information on Percentages In mathematics, the use of a fraction of any number is called a percentage. In everyday life, the individual tends to interact with percentages all the time if it is necessary to count the number of discounts, the amount of a loan payment, or premium deductions to a paycheck. The concept of “percent” in general is one of the essential tools of mathematics since it allows us to quantitatively perceive fractions of the whole in order to compare them later. In general, a percent is commonly referred to as one-hundredth of a part in relation to the whole, denoted by the special symbol “%.” For example, one of the tasks of percentage mathematics may be to use the following calculation scheme shown in the equation [1]. It is known that the average human body mass is 70 kg, of which 3 kg is occupied by the head. What is the mass percentage of