Compound and Simple Interest

Interest problems appear in nearly every placement test. The key distinction: simple interest is calculated only on the principal, while compound interest is calculated on the principal plus accumulated interest.

Simple Interest (SI)

SI = (P × R × T) / 100

Where P = principal, R = rate per annum (%), T = time in years.

Example: ₹5,000 at 8% for 3 years.

SI = (5000 × 8 × 3) / 100 = ₹1,200
Total amount = 5000 + 1200 = ₹6,200

Compound Interest (CI)

A = P × (1 + R/100)^T
CI = A - P = P × [(1 + R/100)^T - 1]

Example: ₹5,000 at 8% compounded annually for 3 years.

A = 5000 × (1.08)^3 = 5000 × 1.259712 = ₹6,298.56
CI = 6298.56 - 5000 = ₹1,298.56

Simple vs Compound Comparison

Key insight: The difference grows over time because CI earns interest on interest.

Key Formulas

Compounding More Than Once a Year

A = P × (1 + R/(n × 100))^(n × T)

Where n = number of compounding periods per year.

Example: ₹10,000 at 12% compounded quarterly for 1 year.

A = 10000 × (1 + 12/(4×100))^4 = 10000 × (1.03)^4 = ₹11,255.09

Effective Annual Rate

Effective rate = (1 + R/(n×100))^n - 1

For 12% compounded quarterly: (1.03)^4 - 1 = 12.55% effective rate.

Shortcuts

Shortcut 1: If CI and SI on the same principal at the same rate for 2 years are given, the difference equals:

CI - SI = P × (R/100)^2

Shortcut 2: For 3 years, the difference equals:

CI - SI = P × (R/100)^2 × (3 + R/100)

Practice Questions

Q1: ₹8,000 at 5% CI for 2 years. Find CI.

A = 8000 × (1.05)^2 = 8000 × 1.1025 = ₹8,820
CI = 8820 - 8000 = ₹820

Q2: A sum doubles in 10 years at SI. Find the rate.

2P = P + P × R × 10/100
P = P × R × 10/100
R = 10%

Q3: If CI on ₹5,000 for 2 years is ₹820, find the rate.

A = 5820, so (1 + R/100)^2 = 5820/5000 = 1.164
1 + R/100 = √1.164 = 1.079
R = 7.9% ≈ 8%

Summary Table

Cross-references

• Percentages
• Profit and loss
• Ratios and proportions
• Averages