DFA1113_Lecture1_Financial_Mathematics 2

Today, we're delving into the intricate world of Financial Mathematics, specifically focusing on how mathematical functions help us understand and predict economic behaviors. We'll explore linear functions, which are fundamental in illustrating a constant rate of change between variables. For instance, in a graduate salary projection, a linear function can model a fresh finance graduate's income, starting at 20,000 Rs/month with a fixed annual raise of 1,000 Rs. This means their salary after 'n' years can be simply calculated as S(n) = 20,000 + 1,000n. If we want to know how many years it takes to reach Rs 25,000, we set the equation to 25,000 = 20,000 + 1,000n, which simplifies to 5,000 = 1,000n, meaning it takes 5 years to achieve that salary level. Another application of linear functions is in total operating cost, where a firm might have a fixed overhead plus variable production costs per unit. For example, if a company has 15,000 Rs in fixed overhead and variable costs of 50 Rs per unit, the total cost C(q) for producing 'q' units is C(q) = 50q + 15,000. If we produce 400 units, the total cost would be C(400) = 50(400) + 15,000 = 20,000 + 15,000 = 35,000 Rs. Conversely, if we have an output level for 50,000 Rs, we can find the quantity 'q' by solving 50,000 = 50q + 15,000, leading to 35,000 = 50q, and thus q = 700 units. These examples clearly demonstrate the practical utility of linear functions in financial analysis and forecasting. Understanding these basic principles allows us to model various economic scenarios with precision and foresight.