CI and SI Together: Difference, Comparison and Instalments
CI and SI Together: Difference, Comparison and Instalments
The most-repeated NTPC interest question of recent cycles is the difference between CI and SI on the same sum: it came in 2021, 2022, June 2025 and March 2026. The difference is just "interest on interest", which gives clean formulas for 2 and 3 years. This page also covers finding the rate when both CI and SI are given, comparing them, and equal instalments (CBT-2 level).
1. Difference Formulas
2 years: CI − SI = P × (R/100)²
3 years: CI − SI = P × (R/100)² × (3 + R/100) = P × R² × (300 + R)/100³
| Rate | Difference for 2 years (% of P) | Difference for 3 years (% of P) |
|---|---|---|
| 4% | 0.16% | 0.4864% |
| 5% | 0.25% | 0.7625% |
| 8% | 0.64% | 1.9712% |
| 10% | 1% | 3.1% |
| 12% | 1.44% | 4.4928% |
Why it works: in year 2, CI also earns interest on the first year's interest, which is P × R/100 × R/100.
2. When Both SI and CI for 2 Years Are Given
Rate R = (CI − SI)/(SI for one year) × 100 = 2(CI − SI)/(SI for 2 years) × 100
Then P = (SI for one year) × 100/R
3. Equal Annual Instalments (CBT-2 Level)
Under CI, each instalment x paid at the end of year k is worth x/(1 + R/100)ᵏ today. The loan equals the sum of these present values:
Loan = x/(1 + R/100) + x/(1 + R/100)² + ... + x/(1 + R/100)ⁿ
For 10%: 2 instalments: loan = x × (1/1.1 + 1/1.21) = x × 2.1/1.21; 3 instalments: x × (1/1.1 + 1/1.21 + 1/1.331).
✗ CI − SI for 3 years = 3 × (CI − SI for 2 years) | ✓ Use P(R/100)²(3 + R/100); at 10% the 3-year difference is 3.1% of P, not 3%
✗ Equal instalments = (loan + total CI)/n | ✓ Instalments are discounted to the present year by year; the simple split overpays
हिंदी नोट: दो वर्ष के लिए चक्रवृद्धि और साधारण ब्याज का अंतर P(R/100)² होता है, क्योंकि दूसरे वर्ष में पहले वर्ष के ब्याज पर भी ब्याज मिलता है। तीन वर्ष के लिए इसे (3 + R/100) से गुणा करें।
Exam Pointer: Verified NTPC patterns: CI − SI for 2 or 3 years, including finding the sum from the difference (January 2021, March 2021, June 2022 CBT-2, two June 2025 Graduate CBT-1 shifts, March 2026 Graduate CBT-1), and SI from a given CI on the same sum (April 2021). Rate-from-both-interests and instalments had no verified NTPC shift in our check and are tagged syllabus-based; instalments sit in the CBT-2 block.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Difference between CI and SI for 2 or 3 years
[PYQ: NTPC Graduate CBT-1 24-Mar-2026 Shift-1 | NTPC Graduate CBT-1 9-Jun-2025 Shift-2 | NTPC CBT-1 4-Jan-2021 Shift-1]
EXAM LEVEL
Q. Find the difference between compound interest and simple interest on ₹15,000 at 8% per annum for 2 years.
Difference = 15,000 × (8/100)² = 15,000 × 0.0064 = ₹96.
Answer: ₹96
EXAMATLAS LEVEL
Q. Find the difference between CI and SI on ₹20,000 at 10% per annum for 3 years, and the sum on which the 2-year difference at 12% would be ₹288.
3 years: 20,000 × (0.1)² × 3.1 = ₹620 (CI ₹6,620, SI ₹6,000). For the second part, P × (0.12)² = 288 gives P × 0.0144 = 288 and P = ₹20,000.
Answer: ₹620; ₹20,000
Pattern 2: Both SI and CI for 2 years given: find the rate and the sum
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. On a certain sum, simple interest for 2 years is ₹1,200 and compound interest for 2 years at the same rate is ₹1,260. Find the rate and the sum.
One year's SI = ₹600. The extra ₹60 is interest on ₹600 for one year, so R = 60/600 × 100 = 10%. P = 600 × 100/10 = ₹6,000.
Answer: 10%; ₹6,000
EXAMATLAS LEVEL
Q. The compound interest on a sum for 2 years is ₹2,544 and the simple interest for 2 years at the same rate is ₹2,400. Find the rate and the sum.
Yearly SI = ₹1,200; CI − SI = ₹144 = interest on 1,200 for a year, so R = 144/1,200 × 100 = 12%. P = 1,200 × 100/12 = ₹10,000. Check: 10,000 × 1.2544 − 10,000 = 2,544.
Answer: 12%; ₹10,000
Pattern 3: CI compared with SI on the same sum
[PYQ: NTPC CBT-1 1-Apr-2021 Shift-2]
EXAM LEVEL
Q. The compound interest on a sum for 2 years at 10% per annum is ₹2,100. Find the simple interest on the same sum at the same rate for the same time.
CI for 2 years at 10% = 21% of P, so P = ₹10,000. SI = 20% of 10,000 = ₹2,000. Shortcut: SI = CI × 20/21.
Answer: ₹2,000
EXAMATLAS LEVEL
Q. For 3 years at 10% per annum, find the ratio of compound interest to simple interest on the same sum, and the sum for which their difference is ₹465.
CI = 33.1% of P and SI = 30% of P, ratio 331 : 300. Difference = 3.1% of P = 465, so P = ₹15,000.
Answer: 331 : 300; ₹15,000
CBT-2 LEVEL
Pattern 4: Equal annual instalments under CI
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A loan of ₹21,000 at 10% compound interest is repaid in 2 equal annual instalments. Find each instalment.
21,000 = x/1.1 + x/1.21 = x × (1.1 + 1)/1.21 = x × 2.1/1.21. So x = 21,000 × 1.21/2.1 = ₹12,100.
Answer: ₹12,100
EXAMATLAS LEVEL
Q. A loan of ₹33,100 at 10% per annum compound interest is repaid in 3 equal annual instalments. Find each instalment.
33,100 = x(1/1.1 + 1/1.21 + 1/1.331). Multiply by 1.331: 33,100 × 1.331 = x(1.21 + 1.1 + 1) = 3.31x. So x = 44,056.1/3.31 = ₹13,310. Check: present values 12,100 + 11,000 + 10,000 = 33,100.
Answer: ₹13,310
60-Second Revision
- CI − SI: 2 years P(R/100)²; 3 years P(R/100)²(3 + R/100).
- Given 2-year SI and CI: R = (CI − SI) ÷ one year's SI × 100.
- 10% for 2 years: CI 21%, SI 20%; for 3 years: 33.1% and 30%.
- Instalments: loan = sum of x/(1 + R/100)ᵏ for k = 1 to n.
Next Step: Simple and Compound Interest done. Practise the interest questions in the ExamAtlas RRB NTPC 2026 mock tests next; the CI − SI difference alone has come in at least six verified shifts.