Study Notes: Interest (Simple and Compound)

Overview

Interest is the extra money paid for borrowing or earned by lending a sum of money over time. In SSC GD, you'll face 3–5 direct questions on this topic, making it a crucial scoring area. The exam tests two main types: **Simple Interest (SI)**, where interest stays constant each year, and **Compound Interest (CI)**, where interest is calculated on the accumulated amount. Mastery requires understanding the formulas, recognizing which type applies, and executing time-based calculations accurately. Most questions involve finding principal, rate, time, or the interest itself. A few tricky problems combine SI and CI or ask for the difference between them. With systematic practice, this topic becomes a reliable mark-getter because the formulas are fixed and the arithmetic is straightforward.

The key challenge is not the concept but careful substitution and avoiding calculation errors under time pressure. You must also handle variations like half-yearly or quarterly compounding in CI problems. Strong command here directly boosts your Elementary Mathematics score, and the logical thinking transfers to percentage and ratio topics as well.

Key Concepts

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

• **Rate of Interest (R)**: The percentage charged per time period (usually per annum). Always express rate as a percentage in formulas; for example, 5% means R = 5.

• **Time (T)**: The duration for which money is borrowed or invested, typically in years. Convert months into years by dividing by 12 if needed.

• **Simple Interest (SI)**: Interest calculated only on the principal throughout the entire period. It remains the same every year and does not compound.

• **Compound Interest (CI)**: Interest calculated on the principal plus any interest already earned. The amount grows exponentially because each period's interest becomes part of the next period's principal.

• **Amount (A)**: The total money after adding interest to the principal. For SI, A = P + SI. For CI, amount is calculated using the compound formula directly.

• **Compounding Frequency**: CI can be calculated annually, half-yearly, quarterly, or monthly. Adjust the rate and time accordingly: if half-yearly, double the time and halve the rate.

• **Difference between CI and SI**: For the same P, R, and T, CI is always greater than SI (except for T = 1 year when they are equal). The difference grows with time.

Formulas / Key Facts

**Simple Interest:**

• SI = (P × R × T) / 100
• Amount A = P + SI = P(1 + RT/100)
• Principal P = (SI × 100) / (R × T)
• Rate R = (SI × 100) / (P × T)
• Time T = (SI × 100) / (P × R)

**Compound Interest (Annual Compounding):**

• Amount A = P(1 + R/100)^T
• CI = A - P = P[(1 + R/100)^T - 1]
• If compounded half-yearly: A = P(1 + R/200)^(2T)
• If compounded quarterly: A = P(1 + R/400)^(4T)

**Special Formula (CI for 2 years):**

• CI for 2 years = P × R × (200 + R) / 10000

**Special Formula (CI for 3 years):**

• CI for 3 years = P × R × (300 + 3R + R²/100) / 10000

**Difference between CI and SI for 2 years:**

• CI - SI = P(R/100)²

**Difference between CI and SI for 3 years:**

• CI - SI = P × R² × (300 + R) / 1000000

Worked Examples

**Example 1 (Simple Interest):** A person borrows ₹8000 at 5% per annum simple interest for 3 years. Find the total amount to be repaid.

**Solution:** Given: P = 8000, R = 5%, T = 3 years SI = (P × R × T) / 100 = (8000 × 5 × 3) / 100 = 120000 / 100 = ₹1200 Amount = P + SI = 8000 + 1200 = ₹9200

**Example 2 (Compound Interest):** Find the compound interest on ₹10000 at 10% per annum for 2 years compounded annually.

**Solution:** Given: P = 10000, R = 10%, T = 2 years Amount A = P(1 + R/100)^T = 10000(1 + 10/100)² = 10000(1.1)² = 10000 × 1.21 = ₹12100 CI = A - P = 12100 - 10000 = ₹2100

Alternatively using special formula: CI = P × R × (200 + R) / 10000 = 10000 × 10 × 210 / 10000 = ₹2100

**Example 3 (Half-yearly Compounding):** What is the compound interest on ₹5000 at 8% per annum for 1 year compounded half-yearly?

**Solution:** For half-yearly: Rate becomes R/2 = 4%, Time becomes 2T = 2 half-years A = P(1 + R/200)^(2T) = 5000(1 + 4/100)² = 5000(1.04)² = 5000 × 1.0816 = ₹5408 CI = 5408 - 5000 = ₹408

**Example 4 (Finding Principal):** Simple interest on a sum for 4 years at 6% per annum is ₹1440. Find the principal.

**Solution:** SI = 1440, R = 6%, T = 4 years P = (SI × 100) / (R × T) = (1440 × 100) / (6 × 4) = 144000 / 24 = ₹6000

Common Mistakes

**Wrong formula selection → Check whether the problem says "simple" or "compound"**. Read carefully; if nothing is specified, assume simple interest unless the context (like bank deposits) suggests compounding. Don't mix SI and CI formulas.

**Forgetting to convert time units → Always express time in years when using standard formulas**. If time is given as 6 months, write T = 6/12 = 0.5 years. Similarly, 18 months = 1.5 years. Mismatched units destroy the entire calculation.

**Wrong adjustment for half-yearly/quarterly → Students often forget to modify both rate and time**. For half-yearly: halve the rate AND double the time periods. For quarterly: divide rate by 4 AND multiply time by 4. Both adjustments must happen together.

**Confusing Amount and Interest → Amount includes both principal and interest; interest is only the extra paid**. When asked for CI or SI, calculate the interest separately (A - P), don't report the amount as interest.

**Rounding errors in compound calculations → Compound interest involves powers and multiple multiplications**. Keep at least two decimal places during intermediate steps. Rounding too early (especially in the (1 + R/100) term) leads to wrong final answers. Use the special 2-year or 3-year formulas when possible to reduce calculation load.

Quick Reference

• SI = (P × R × T) / 100; grows linearly each year.
• CI amount: A = P(1 + R/100)^T; interest compounds on interest.
• For 2 years, CI - SI = P(R/100)² — useful shortcut for difference questions.
• Half-yearly means R/2 and 2T; quarterly means R/4 and 4T.
• Always subtract principal from amount to get the actual interest earned.
• If time or rate doubles, SI doubles; CI more than doubles due to compounding effect.