1. Let's start with **sets and set theory**. A set is a collection of distinct objects, called elements. For example, $A = \{1, 2, 3\}$ is a set with elements 1, 2, and 3. 2. **Simple Interest** is calculated on the original principal only. The formula is: $$SI = \frac{P \times R \times T}{100}$$ where $P$ is principal, $R$ is rate of interest per year, and $T$ is time in years. 3. **Commission** is a fee paid to an agent for services, often a percentage of the sale price. If the sale price is $S$ and commission rate is $c\%$, then commission $C = \frac{c}{100} \times S$. 4. **Discount** is a reduction from the marked price. If the marked price is $M$ and discount rate is $d\%$, then discount $D = \frac{d}{100} \times M$ and the selling price is $S = M - D$. 5. **Hire Purchase** is a system where the buyer pays an initial deposit and then installments. The total cost includes interest. If the cash price is $C$, deposit $D$, and balance paid in installments with interest $I$, total paid is $D + (C - D) + I$. 6. **Mortgage** is a loan to buy property, paid back with interest over time. The monthly payment depends on principal, interest rate, and loan term, often calculated using amortization formulas. These concepts are fundamental in finance and mathematics, and understanding their formulas helps solve related problems.