Simple and Compound Interest — SSC MTS Study Notes

Overview

Simple and Compound Interest is a scoring topic in SSC MTS with 1–2 direct questions typically appearing in every exam. The problems test your understanding of how money grows over time under different interest calculation methods. Simple Interest (SI) applies a fixed rate on the principal amount throughout the tenure, while Compound Interest (CI) applies interest on both principal and accumulated interest, leading to exponential growth.

For SSC MTS, you must master the basic formulas for SI and CI with annual compounding, understand half-yearly and quarterly compounding variations, and solve instalment-based problems. The questions are straightforward calculation-based with minimal complexity—accuracy and speed in applying the correct formula matter most. Understanding the difference between SI and CI on the same principal and recognizing when interest is compounded more frequently than annually are key exam skills.

Practice is essential because these problems involve multiple steps: identifying given values (P, R, T), selecting the right formula, calculating powers carefully (especially for CI), and handling unit conversions (years to half-years). A strong grip on this topic guarantees 2–3 marks with minimal effort.

Key Concepts

• **Principal (P)**: The initial sum of money lent or invested. All interest calculations begin with identifying P correctly.

• **Rate of Interest (R)**: The percentage charged per time period, usually per annum. Always convert percentage to decimal or use the formula directly with R as a number.

• **Time Period (T)**: Duration for which money is lent or invested, typically in years. For half-yearly compounding, double the time periods; for quarterly, multiply by four.

• **Simple Interest grows linearly**: The interest earned each period is the same because it is calculated only on the principal, not on accumulated interest.

• **Compound Interest grows exponentially**: Interest is added to principal after each compounding period, and subsequent interest is calculated on this new total (principal + previous interest).

• **Amount (A)**: The total money returned at the end = Principal + Interest. For SI: A = P + SI; for CI: A = P(1 + R/100)^T.

• **Instalment problems**: When a loan is repaid in equal instalments, each instalment pays off part of the principal plus interest. Use the present value approach or the instalment formula to solve.

• **More frequent compounding increases CI**: Half-yearly compounding yields more interest than annual because interest is added twice per year; quarterly adds even more.

Formulas / Key Facts

**Simple Interest (SI)**

• SI = (P × R × T) / 100
• Amount A = P + SI = P(1 + RT/100)
• If SI is given, Principal P = (SI × 100) / (R × T)

**Compound Interest (CI) — Annual Compounding**

• Amount A = P(1 + R/100)^T
• CI = A − P = P[(1 + R/100)^T − 1]
• For two different rates R1 and R2 over two years: A = P(1 + R1/100)(1 + R2/100)

**CI — Half-Yearly Compounding**

• Rate becomes R/2 per half-year; time becomes 2T half-years
• A = P(1 + R/200)^(2T)

**CI — Quarterly Compounding**

• Rate becomes R/4 per quarter; time becomes 4T quarters
• A = P(1 + R/400)^(4T)

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

• CI − SI = P(R/100)² (This is a popular shortcut for 2-year problems)

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

• CI − SI = P(R/100)²(3 + R/100)

**Instalment Formula (Equal Annual Instalments)**

• If loan P is repaid in n equal instalments of x each at rate R% per annum:
• P = x/(1 + R/100) + x/(1 + R/100)² + ... + x/(1 + R/100)^n

Worked Examples

**Example 1: Simple Interest Calculation** Find the SI on ₹8000 at 5% per annum for 3 years.

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

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

*Solution:* P = 10000, R = 10%, T = 2 years 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

*Shortcut Check:* SI for 2 years = (10000 × 10 × 2)/100 = ₹2000 CI − SI = P(R/100)² = 10000(10/100)² = 10000 × 0.01 = ₹100 CI = SI + 100 = 2000 + 100 = ₹2100 ✓

**Example 3: Half-Yearly Compounding** Find the amount on ₹5000 at 8% per annum for 1 year compounded half-yearly.

*Solution:* P = 5000, R = 8% per annum, T = 1 year Half-yearly: Rate = 8/2 = 4% per half-year, Time = 1 × 2 = 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 from SI** At what principal will the SI be ₹600 in 4 years at 5% per annum?

*Solution:* SI = 600, R = 5%, T = 4 years P = (SI × 100) / (R × T) = (600 × 100) / (5 × 4) = 60000 / 20 = ₹3000

Common Mistakes

**Using annual values for half-yearly compounding**: Students often forget to halve the rate and double the time. Always adjust both R and T when compounding is not annual. → **Fix**: For half-yearly, R becomes R/2 and T becomes 2T; for quarterly, R becomes R/4 and T becomes 4T.

**Confusing Amount with Interest**: The question asks for CI but you calculate and write A as the answer. → **Fix**: Always read carefully—if CI is asked, subtract P from A. If Amount is asked, give A directly.

**Wrong power calculation**: For CI, students miscalculate (1 + R/100)^T, especially for T = 3 or fractional powers. → **Fix**: Break down step-by-step: first calculate 1 + R/100, then raise to the power T carefully. Use multiplication for integer powers.

**Applying CI formula to SI problems**: Mixing up which formula to use based on the question type. → **Fix**: Look for keywords—"simple interest" or "SI" means linear formula; "compound interest," "compounded annually/half-yearly" means exponential formula.

**Not converting time units**: If time is given in months and rate is per annum, directly using months in the formula gives wrong results. → **Fix**: Convert months to years (divide by 12) or adjust the rate accordingly before calculation.

Quick Reference

• SI = (P × R × T) / 100; grows linearly, same interest each period.
• CI Amount: A = P(1 + R/100)^T; interest-on-interest effect.
• For 2 years: CI − SI = P(R/100)²—use this shortcut to save time.
• Half-yearly compounding: halve rate, double time → A = P(1 + R/200)^(2T).
• Quarterly compounding: quarter rate, quadruple time → A = P(1 + R/400)^(4T).
• Always identify P, R, T first; choose SI or CI formula based on question keyword.