चक्रवृद्धि ब्याज
Compound Interest
Compound interest is where the exam separates the prepared from the rest, and it brings one to three SBI Clerk questions that reward a good shortcut heavily. Unlike simple interest, each year's interest is added to the principal so the next year earns on a larger base — interest on interest. The direct formula works, but the real speed comes from the two-year and three-year difference tricks that turn a scary sum into a few seconds of mental maths.
The Core Formula
The amount under compound interest is A = P × (1 + R/100)^T, and the interest itself is CI = A − P. For two years at 10%, the factor is (1.1)^2 = 1.21, so 5,000 grows to 6,050 and CI is 1,050. Expanding the power by hand is slow, which is exactly why the difference shortcuts below exist. Use the direct formula only when the time is one or two years and the rate is convenient. When interest is compounded half-yearly, halve the rate and double the time before applying the formula, and for quarterly compounding quarter the rate and quadruple the time — SBI Clerk sometimes slips this in, and candidates who forget to adjust both R and T together get a wrong base.
A = P × (1 + R/100)^T CI = A − P (compounded annually)
CI − SI Difference for 2 and 3 Years
Over two years the compound interest exceeds simple interest by exactly the interest on one year's interest: difference = P × (R/100)^2. Over three years it is P × (R/100)^2 × (3 + R/100). These formulas let you find a principal or rate from the given difference in one line, which is precisely how SBI Clerk frames the harder version — 'the difference between CI and SI for 2 years at 10% is 50, find the sum'.
| Period | CI − SI difference | Example at R = 10% |
|---|---|---|
| 2 years | P × (R/100)² | P/100 → 5,000 gives 50 |
| 3 years | P × (R/100)² × (3 + R/100) | ≈ 0.031 P → 5,000 gives 155 |
| 1 year | 0 (CI = SI) | always equal in year one |
Solved Examples
Example 1: P 5,000, R 10%, T 2 yrs → A = 5000 × 1.21 = 6,050, so CI = 1,050. Example 2: CI − SI for 2 years at 10% is 50, so P × (10/100)² = 50 → P = 5,000. Example 3: The first year's CI and SI are always equal, so any difference given is created entirely in the second year onward.
✗ Adding simple interest each year for a compound sum | ✓ Multiplying by the growth factor (1 + R/100) each year
Fraction Method for Rates Like 1/8
For awkward-looking rates, convert the rate to a fraction and grow the principal step by step. A rate of 12.5% is 1/8, so each year the amount becomes 9/8 of the previous year: 12.5% on 6,400 gives 6,400 × 9/8 = 7,200, and a second year gives 7,200 × 9/8 = 8,100. This 'add one-eighth each year' method beats squaring decimals and matches the fraction table you already know — 6.25% is 1/16, so multiply by 17/16, and 20% is 1/5, so multiply by 6/5. Building the amount as a chain of clean fractions is the fastest reliable way to handle two- and three-year compound sums under exam pressure.
चक्रवृद्धि ब्याज में हर साल का ब्याज मूलधन में जुड़ जाता है: A = P(1 + R/100)^T। 2 वर्ष का CI−SI अंतर = P(R/100)²। दर 12.5% = 1/8, तो हर साल राशि 9/8 गुना।
Exam Pointer — Compound interest gives one to three SBI Clerk marks and is usually asked for two or three years, or as a CI−SI difference sum. The direct power formula is slow, so the examiner effectively rewards the difference shortcuts and the fraction method. Learn P × (R/100)² cold — it cracks most 'find the sum' CI questions in one line.
60-Second Recap
- A = P(1 + R/100)^T; CI = A − P; year-one CI equals SI.
- 2-year CI − SI = P × (R/100)²; use it to find P fast.
- 3-year difference = P × (R/100)² × (3 + R/100).
- Rate as a fraction: 12.5% = 1/8, so grow by 9/8 each year.