Simple and Compound Interest — SSC CHSL Study Notes

Overview

Simple and Compound Interest form a core arithmetic topic in SSC CHSL Tier 1, typically contributing 2–4 questions per exam. Questions test your ability to compute interest over different time periods, handle half-yearly or quarterly compounding, and solve instalment-based problems. Mastery requires fluency with the basic formulas, quick mental calculation for standard rates (10%, 5%, 8%), and pattern recognition for compounding intervals. Unlike complex banking exams, CHSL focuses on direct formula application and one- or two-step word problems. You must differentiate clearly between SI and CI scenarios and understand when interest gets added to principal. Strong performance here boosts your Quantitative Aptitude score with minimal preparation time if you drill the standard problem types.

Key Concepts

• **Simple Interest (SI)** is calculated only on the original principal throughout the loan or deposit period. It does not change year-to-year because interest earned is not reinvested.

• **Compound Interest (CI)** calculates interest on the accumulated amount (principal plus previously earned interest) at the end of each compounding period. The principal effectively grows after each period.

• **Compounding frequency** determines how often interest is added to principal. Annual compounding adds once per year; half-yearly means twice per year; quarterly means four times per year. More frequent compounding results in higher total interest.

• **Instalments** are equal periodic payments made to repay a loan. Each instalment covers part interest and part principal. For CHSL, problems usually involve finding the instalment amount given principal, rate and time.

• **Difference between CI and SI** over the same period and rate is a common question type. This difference arises because CI compounds interest, creating "interest on interest."

• The **effective rate** per compounding period is the annual rate divided by the number of periods per year. For example, 12% per annum compounded quarterly means 3% per quarter.

• Time must always be expressed in the same unit as the rate. If rate is annual, convert months into years (divide by 12) or days into years (divide by 365).

Formulas / Key Facts

**Simple Interest** SI = (P × R × T) / 100 where P = Principal, R = Rate % per annum, T = Time in years.

**Amount under SI** A = P + SI = P (1 + (R × T)/100)

**Compound Interest (annual compounding)** A = P (1 + R/100)^T CI = A − P

**CI with half-yearly compounding** A = P (1 + (R/2)/100)^(2T) Here rate is halved, time (in years) is doubled because there are two periods per year.

**CI with quarterly compounding** A = P (1 + (R/4)/100)^(4T) Rate divided by 4, time multiplied by 4.

**Difference between CI and SI for 2 years** CI − SI = P (R/100)² This shortcut applies only for 2-year problems with annual compounding.