Simple and Compound Interest

Overview

Simple and Compound Interest form a crucial quantitative topic in MP TET, appearing regularly in the Mathematics section. These concepts test your ability to calculate the cost of borrowing money or the returns on savings over time. Understanding the distinction between SI and CI is essential—SI grows linearly while CI grows exponentially due to "interest on interest."

For the exam, you must be comfortable with direct formula application, conversion between SI and CI problems, and word problems involving loans, deposits, and instalments. Questions typically involve 2-3 year periods and may require you to find principal, rate, time, or the difference between SI and CI. Mastery of this topic also builds foundation for profit-loss and percentage problems.

Key Concepts

• **Principal (P)**: The original sum of money borrowed or invested before any interest is added.

• **Rate of Interest (R)**: The percentage charged or earned per unit time, usually expressed as "per annum" (per year).

• **Time (T or n)**: The duration for which money is borrowed or invested, typically in years.

• **Simple Interest (SI)**: Interest calculated only on the original principal throughout the entire period. The interest amount remains constant each year.

• **Compound Interest (CI)**: Interest calculated on principal plus accumulated interest from previous periods. Each year's interest is added to principal, creating a snowball effect.

• **Amount (A)**: The total money at the end of the period = Principal + Interest earned.

• **Compounding Frequency**: CI can be compounded annually, half-yearly (twice a year), quarterly (four times a year), or monthly. More frequent compounding yields higher returns.

• **CI always exceeds SI** for the same principal, rate, and time (when time > 1 year), because CI earns interest on previously earned interest.

Formulas / Key Facts

**Simple Interest:**

• SI = (P × R × T) / 100
• Amount = P + SI = P(1 + RT/100)

**Compound Interest:**

• Amount = P(1 + R/100)ⁿ where n = number of years
• CI = Amount − P = P[(1 + R/100)ⁿ − 1]

**Half-yearly Compounding:**

• Rate becomes R/2, Time becomes 2n
• Amount = P(1 + R/200)²ⁿ

**Quarterly Compounding:**