In-Depth: Compound Interest

CLAT Application & Relevance

Importance: Medium. Appears alongside SI in sets comparing different financial schemes. Questions often ask for the difference between CI and SI.

How it's tested: Comparing maturity amounts of different schemes; finding the effective annual rate for different compounding frequencies; calculating the difference between CI and SI for a given period.

Section 1: Core Concepts & Formulas

Compound Interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It's often called "interest on interest" and leads to faster growth of money compared to simple interest.

Key Definitions

Principal (P): The initial amount invested or borrowed.
Rate of Interest (R): The annual rate at which interest is compounded.
Time (T / n): The total duration for which the money is invested/borrowed. In CI, 'n' often represents the number of compounding periods.
Amount (A): The total value after 'n' periods, including principal and accumulated interest.

Fundamental Formulas

Amount (A) when compounded Annually: A = P * (1 + R/100)^T
Compound Interest (CI) = A - P
When compounded Half-Yearly: Rate becomes R/2, Time (number of periods) becomes 2T. Formula: A = P * (1 + (R/2)/100)^(2T)
When compounded Quarterly: Rate becomes R/4, Time (number of periods) becomes 4T. Formula: A = P * (1 + (R/4)/100)^(4T)
Difference between CI and SI for 2 years: Difference = P * (R/100)^2
Difference between CI and SI for 3 years: Difference = P * (R/100)^2 * (3 + R/100)

Section 2: Solved CLAT-Style Examples

Example 1: Basic CI Calculation (Annually)

Passage Context: A young legal professional invests ₹80,000 in a new-age investment fund that promises a return of 10% per annum, compounded annually.

Question: "What will be the total amount in their account after 2 years?"

Detailed Solution:
1. Identify Given Values: Principal (P) = ₹80,000 Rate (R) = 10% per annum Time (T) = 2 years
2. Apply the Amount Formula (Annually): A = P * (1 + R/100)^T
A = 80000 * (1 + 10/100)^2
A = 80000 * (1.1)^2
A = 80000 * 1.21
3. Calculate: A = ₹96,800.
Answer: The total amount after 2 years will be ₹96,800.

Example 2: Comparing CI and SI for a Given Period

Passage Context: An NGO receives a grant of ₹1,00,000. They consider two investment options: Scheme A offers 8% simple interest annually, and Scheme B offers 8% compound interest annually.

Question: "What is the difference in the interest earned between Scheme B (CI) and Scheme A (SI) after 3 years?"

Detailed Solution:
1. Calculate SI for 3 years: SI = (P * R * T) / 100 SI = (100000 * 8 * 3) / 100 SI = ₹24,000.
2. Calculate CI for 3 years: Using the difference formula directly for 3 years: Difference = P * (R/100)^2 * (3 + R/100) Difference = 100000 * (8/100)^2 * (3 + 8/100) Difference = 100000 * (0.08)^2 * (3 + 0.08) Difference = 100000 * 0.0064 * 3.08 Difference = 640 * 3.08 = ₹1,971.20.
(Alternatively, calculate CI total amount: A = 100000 * (1.08)^3 = 100000 * 1.259712 = 125971.20. So CI = 125971.20 - 100000 = 25971.20. Then CI - SI = 25971.20 - 24000 = ₹1,971.20.)
Answer: The difference in interest earned after 3 years is ₹1,971.20.