Master Simple and Compound Interest for CBSE Class 11 Applied Mathematics. Learn formulas, step-by-step solutions, and exam-style practice problems.
Simple interest is calculated only on the principal amount for the entire duration of the loan or investment. It is a linear growth model where the interest remains constant for each period. This is commonly used in short-term personal loans or specific government bonds.
Step 1: Identify P = 5000, R = 8%, T = 3 years.
Step 2: Apply formula SI = (5000 × 8 × 3) / 100.
Step 3: Calculate 120000 / 100 = 1200.
Answer: The simple interest is ₹1200.
Compound interest is calculated on the principal plus the accumulated interest from previous periods, leading to exponential growth. The frequency of compounding, such as annually, semi-annually, or quarterly, significantly impacts the final amount. It is the standard for savings accounts and long-term investments.
Step 1: P = 10000, R = 10%, n = 1 (annually), t = 2 years.
Step 2: A = 10000(1 + 0.10/1)².
Step 3: A = 10000(1.1)² = 10000 × 1.21 = 12100.
Answer: The total amount is ₹12100.
The effective annual rate (EAR) converts the nominal interest rate into an equivalent annual rate considering the compounding frequency. This allows for direct comparison between different investment schemes with varying compounding periods. It is calculated using the formula involving the nominal rate and frequency.
Step 1: Nominal rate R = 12% (0.12), compounded quarterly (n = 4).
Step 2: EAR = (1 + 0.12/4)⁴ − 1.
Step 3: EAR = (1.03)⁴ − 1 = 1.1255 − 1 = 0.1255.
Answer: The effective annual rate is 12.55%.