Compound Interest Guide & Practice
Master CI formula, half-yearly and quarterly compounding, CI vs SI difference, and installment calculations with solved examples and mock tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.
Practice Question Papers
Practice Filters
1. Fundamentals & Definitions
- Principal (P): The original sum of money borrowed or lent.
- Interest (I): The extra money paid for using the principal.
- Time (T): The duration for which the principal is borrowed or lent, typically in years.
- Rate of Interest (R): The percentage at which interest is calculated on the principal per unit of time (usually per annum).
- Amount (A): The total sum of money due at the end of the time period, which is the Principal plus the Interest.
A = P + I. - Compound Interest (CI): Interest calculated on the initial principal and also on the accumulated interest of previous periods. The interest for a new period is computed on a principal that includes the interest from the previous period.
2. Core Concepts & Formulas
General Formula for Compound Interest
The fundamental formula to calculate the Amount (A) when interest is compounded is: A = P (1 + R/100)T
Where:
- A = Amount
- P = Principal
- R = Rate of Interest (per annum)
- T = Time (in years)
The Compound Interest (CI) is the difference between the Amount and the Principal: CI = A - P CI = P [ (1 + R/100)T - 1 ]
Compounding Frequency
If the interest is not compounded annually, the formula is adjusted: A = P (1 + (R/n) / 100)n*T
Where n is the number of times interest is compounded per year.
| Compounding Frequency | n | Rate (R) becomes | Time (T) becomes |
|---|---|---|---|
| Annually | 1 | R | T |
| Half-Yearly (Semi-Annually) | 2 | R/2 | 2T |
| Quarterly | 4 | R/4 | 4T |
Rule of 72
A quick method to estimate the number of years required to double an investment at a given annual rate of return. Years to Double ≈ 72 / Interest Rate
Difference between Compound Interest and Simple Interest
For a period of 2 years, the difference is given by: CI - SI = P * (R/100)2
For a period of 3 years, the difference is given by: CI - SI = P * (R/100)2 * (R/100 + 3)
Typical Exam Weightage
| Exam | Typical Questions |
|---|---|
| SSC (CGL / CHSL / MTS) | 1 question |
| Banking (IBPS / SBI) | 1–2 questions |
| Railways (RRB) | 1 question |
Often tested together with Simple Interest in a comparative (CI vs SI difference) question.
Figures are typical ranges based on recent-year patterns, not a guarantee for any specific upcoming paper — always cross-check against the latest official syllabus and previous-year papers for Compound Interest.
Solved Examples
Question: Find the compound interest on ₹10,000 for 2 years at a rate of 4% per annum.
View Detailed Solution & ExplanationHide Explanation
- Given:
- Principal (P) = ₹10,000
- Rate (R) = 4% per annum
- Time (T) = 2 years
- Formula: Amount (A) = P (1 + R/100)T
- Calculation:
- A = 10000 * (1 + 4/100)2
- A = 10000 * (1 + 1/25)2
- A = 10000 * (26/25)2
- A = 10000 * (676 / 625)
- A = 16 * 676
- A = ₹10,816
- Compound Interest (CI):
- CI = Amount - Principal
- CI = 10816 - 10000
- CI = ₹816
Question: What is the compound interest on a sum of ₹8,000 for 1 year at 10% per annum, if the interest is compounded half-yearly?
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- Given:
- Principal (P) = ₹8,000
- Annual Rate (R) = 10% per annum
- Time (T) = 1 year
- Compounding is half-yearly:
- The effective rate becomes R/2 = 10%/2 = 5% per half-year.
- The effective time becomes 2T = 2 * 1 = 2 half-years.
- Formula: A = P (1 + R/100)T
- Calculation:
- A = 8000 * (1 + 5/100)2
- A = 8000 * (1 + 1/20)2
- A = 8000 * (21/20)2
- A = 8000 * (441 / 400)
- A = 20 * 441
- A = ₹8,820
- Compound Interest (CI):
- CI = Amount - Principal
- CI = 8820 - 8000
- CI = ₹820
Question: The difference between the compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is ₹40. Find the principal sum.
View Detailed Solution & ExplanationHide Explanation
- Given:
- Difference (CI - SI) = ₹40
- Rate (R) = 5% per annum
- Time (T) = 2 years
- Formula for the difference for 2 years:
- CI - SI = P * (R/100)2
- Calculation:
- 40 = P * (5/100)2
- 40 = P * (1/20)2
- 40 = P * (1/400)
- Solving for P:
- P = 40 * 400
- P = ₹16,000
- The principal sum is ₹16,000.