This page covers SSC MTS Half-Yearly / Quarterly CI with complete concept notes, 15 graded practice MCQs, key points and exam-specific tips. Free to study.
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
15graded MCQs · easy to hard · full solution & trap analysis
₹12,000 is invested at 10% per annum compound interest, compounded quarterly. What is the amount after 9 months?
Practice 2easy
₹20,000 is invested at 20% per annum compound interest, compounded quarterly. What is the compound interest earned in 6 months?
Practice 3easy
A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What is the amount after 1 year?
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 ₹10,404 in 1 year at 8% per annum compound interest, compounded half-yearly. What is the principal?
Practice 6medium
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 7medium
₹12,000 is lent at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 6 months.
Practice 8medium
A principal amount becomes ₹15,625 in 1 year at 20% per annum compound interest, compounded half-yearly. What is the principal?
Practice 9medium
₹20,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the amount after 6 months and the principal?
Practice 10medium
The compound interest on ₹10,000 for 1 year at 10% per annum, compounded half-yearly, is how much more than the simple interest for the same period and rate?
Practice 11hard
A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the compound interest earned in 1.5 years?
Practice 12hard
₹12,000 is invested at 8% per annum compound interest, compounded quarterly. After 2 years, what is the total amount?
Practice 13hard
A certain sum becomes ₹19,360 in 1.5 years at 20% per annum compound interest, compounded half-yearly. What was the original principal?
Practice 14hard
A sum of money doubles itself in 3 years at compound interest, compounded quarterly. What is the rate of interest per annum (approximately)?
Practice 15hard
₹10,000 is invested at 16% per annum compound interest, compounded half-yearly. In how many years will the amount become ₹40,000?
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