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SSC CHSL Half-Yearly / Quarterly CI

Study Material — 2 PYQs (2018–2018) · Concept Notes · Shortcuts

SSC CHSL Half-Yearly / Quarterly CI is a frequently tested subtopic — 2 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

2 PYQs
2018–2018
23 Practice
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6 Key Points
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Previous Year Questions

SSC CHSL Half-Yearly / Quarterly CI — Past Exam Questions

2 questions from actual SSC CHSL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

A sum of ₹8,000 is invested at 10% per annum compounded half-yearly for 1 year. What is the compound interest earned?

Exam Q 22018Previous Year Pattern

A sum of ₹16,000 is invested at 10% per annum compounded half-yearly. What is the compound interest accrued after 1.5 years?

Concept Notes

Half-Yearly / Quarterly CI— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

When you deposit money in a bank, the bank usually adds interest once a year. But some banks add interest twice a year (half-yearly) or four times a year (quarterly). Each time interest is added, it becomes part of the new principal, and the next interest is calculated on this larger amount. This is why more frequent compounding gives you more interest

Key Rules

For half-yearly CI: The rate is divided by 2, and time is multiplied by 2. For quarterly CI: The rate is divided by 4, and time is multiplied by 4

Formula

A = P × (1 + R/(100×n))^(t×n) Where: - A = Amount after interest - P = Principal (original money) - R = Annual rate of interest (%) - n = Number of times compounded per year (2 for half-yearly, 4 for quarterly) - t = Time in years - CI = A − P

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL typically asks: Compare CI for different compounding periods, find CI amount, or calculate effective rate. Shortcut/Trick: For half-yearly: Use R/2 and 2t. For quarterly: Use R/4 and 4t. Always remember the rate gets divided and time gets multiplied by the same number.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Identify n = 4 (quarterly)

2
Step 2

Apply formula: A = 8000 × (1 + 20/(100×4))^(1×4)

3
Step 3

A = 8000 × (1 + 5/100)^4

4
Step 4

A = 8000 × (1.05)^4

5
Step 5

A = 8000 × 1.2155 = 9724

6
Step 6

CI = 9724 − 8000 = Rs 1724

Exam TrapsCommon mistakes students make — avoid these

Students forget to divide the rate by the compounding frequency. They use the full annual rate instead of R/2 or R/4, leading to wrong answers. Always reduce the rate first.

Key Points to Remember

  • Half-yearly CI: Divide rate by 2, multiply time by 2
  • Quarterly CI: Divide rate by 4, multiply time by 4
  • Formula: A = P(1 + R/(100n))^(tn) where n = compounding frequency
  • More frequent compounding = higher final amount
  • CI = Amount − Principal (always calculate both separately)
  • In 1 year, quarterly compounding gives more interest than half-yearly

Exam-Specific Tips

  • For half-yearly compounding, the effective rate formula is: (1 + R/200)^2 − 1
  • For quarterly compounding in 1 year, total compounding periods = 4
  • Half-yearly means n = 2, so rate becomes R/2 for each period
  • Quarterly means n = 4, so rate becomes R/4 for each period
  • If time is 2 years with quarterly compounding, total periods = 8
  • Compound Interest formula with frequency: A = P(1 + r/100)^n where r is periodic rate and n is total periods
  • For half-yearly: 1 year = 2 periods, 2 years = 4 periods, 3 years = 6 periods
Practice MCQs

Half-Yearly / Quarterly CI — Practice Questions

23graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 23

All MCQs →
Practice 1easy

What is the compound interest on ₹5,000 at 8% per annum for 1 year, compounded quarterly?

Practice 2easy

A principal amount becomes ₹6,760 after 2 years at 10% per annum compound interest, compounded half-yearly. What was the principal?

Practice 3easy

At what rate per annum will ₹4,000 amount to ₹4,410 in 1 year, if the interest is compounded half-yearly?

Practice 4easy

₹5,000 is invested at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 6 months.

Practice 5easy

A principal amount becomes ₹10,648 in 2 years at 8% per annum compound interest, compounded half-yearly. What is the principal?

Practice 6easy

₹12,000 is invested at 10% per annum compound interest, compounded half-yearly. What is the compound interest earned in the first 6 months?

Practice 7easy

A sum becomes ₹6,655 after 1 year at 10% per annum compound interest, compounded quarterly. What is the original principal?

Practice 8easy

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1 year?

Practice 9easy

₹20,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1.5 years?

Practice 10medium

₹5,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the compound interest for the first quarter and the second quarter?

Practice 11medium

The difference between compound interest (compounded quarterly) and simple interest on ₹10,000 at 16% per annum for 1 year is:

Practice 12medium

A principal amount becomes ₹15,625 after 2 years at 20% per annum compound interest, compounded half-yearly. What is the principal?

Practice 13medium

₹12,000 is invested at 8% per annum compound interest, compounded quarterly. Find the compound interest earned after 6 months.

Practice 14medium

₹6,400 is invested at a certain rate per annum compound interest, compounded quarterly. If the amount becomes ₹8,100 after 1 year, what is the rate of interest per annum?

Practice 15medium

A principal amount becomes ₹15,625 in 1 year when invested at 20% per annum compound interest, compounded half-yearly. What was the original principal?

Practice 16hard

A principal amount doubles in 5 years at a certain rate of compound interest, compounded half-yearly. What will be the amount after 10 years at the same rate?

Practice 17hard

The difference between compound interest and simple interest on a sum for 2 years at 8% per annum, compounded half-yearly, is ₹61.44. What is the principal?

Practice 18hard

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1.5 years?

Practice 19hard

₹12,000 is lent at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 2 years.

Practice 20hard

A certain sum becomes ₹18,522 in 2 years at 10% per annum compound interest, compounded half-yearly. What is the principal?

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60-Second Revision — Half-Yearly / Quarterly CI

  • Remember: Divide rate by compounding frequency (2 for half-yearly, 4 for quarterly), multiply time by the same number
  • Formula: A = P × (1 + R/(100×n))^(t×n) — this works for ALL compounding frequencies
  • Trap: Don't forget CI = Amount − Principal; calculate both separately
  • Quick Check: In 1 year with quarterly CI at 20% p.a., effective rate ≈ 21.55% (not 20%)
  • Pattern: More frequent compounding always gives MORE interest for same P, R, and t
  • Always verify: After substitution, ensure exponent = compounding periods per year × time in years
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