Question 1

A sum of ₹5,000 is invested at 10% per annum. What is the difference between the compound interest and simple interest earned over 2 years?

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1,000. Step 2: Calculate Compound Interest using A = P(1 + R/100)^T = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050, so CI = 6050 - 5000 = ₹1,050. Step 3: Difference = CI - SI = 1050 - 1000 = ₹50.

Question 2

The difference between compound interest and simple interest on a principal of ₹8,000 at 5% per annum for 2 years is ₹X. Find X.

Accepted Answer

Step 1: SI = (8000 × 5 × 2) / 100 = ₹800. Step 2: A = 8000(1.05)^2 = 8000 × 1.1025 = ₹8,820, so CI = 8820 - 8000 = ₹820. Step 3: Difference = 820 - 800 = ₹20.

Question 3

A principal amount earns ₹500 as simple interest in 2 years at 10% per annum. If the same principal is invested at the same rate for the same period under compound interest, what will be the difference between CI and SI?

Accepted Answer

Step 1: From SI formula, P = (SI × 100) / (R × T) = (500 × 100) / (10 × 2) = ₹2,500. Step 2: SI = ₹500 (given). Step 3: A = 2500(1.10)^2 = 2500 × 1.21 = ₹3,025, so CI = 3025 - 2500 = ₹525. Step 4: Difference = 525 - 500 = ₹25.

Question 4

A sum of ₹10,000 is invested at 8% per annum for 3 years. By how much does the compound interest exceed the simple interest?

Accepted Answer

Step 1: SI = (10000 × 8 × 3) / 100 = ₹2,400. Step 2: A = 10000(1.08)^3 = 10000 × 1.259712 ≈ ₹12,597.12, so CI ≈ ₹2,597.12. Step 3: Difference ≈ ₹197.12 ≈ ₹197 (rounding to nearest rupee).

Question 5

At what rate of interest per annum will the difference between CI and SI on ₹4,000 for 2 years be ₹40?

Accepted Answer

Step 1: Use the formula for difference: CI - SI = P × R² / (100)² for 2 years (approximately). More precisely: SI = (4000 × R × 2)/100 = 80R. Step 2: A = 4000(1 + R/100)^2, so CI = 4000[(1 + R/100)^2 - 1] = 4000[2R/100 + R²/10000] = 80R + 4R²/100. Step 3: Difference = 4R²/100 = 40, so R² = 1000, but let's verify: 4R²/100 = 40 means R² = 1000... Let me recalculate: For 2 years, CI - SI = PR²/10000 = 4000 × R²/10000 = 2R²/5. Setting this equal to 40: 2R²/5 = 40, so R² = 100, thus R = 10% per annum.

Question 6

The difference between compound interest and simple interest on a certain principal for 2 years at 12% per annum is ₹144. What is the principal?

Accepted Answer

Step 1: For 2 years, the difference formula is: CI - SI = P × R² / (100)². Step 2: Substitute values: 144 = P × (12)² / (100)² = P × 144 / 10000. Step 3: Solve for P: P = (144 × 10000) / 144 = ₹10,000.

Question 7

A sum of ₹8,000 is invested at 12% per annum. What is the difference between the compound interest and simple interest earned over 2 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (8000 × 12 × 2) / 100 = ₹1,920. Step 2: Calculate Compound Interest: A = P(1 + R/100)^T = 8000(1.12)^2 = 8000 × 1.2544 = ₹10,035.20. CI = 10,035.20 - 8,000 = ₹2,035.20. Step 3: Difference = CI - SI = 2,035.20 - 1,920 = ₹115.20.

Question 8

Two sums are invested at 10% per annum. Sum A earns simple interest and Sum B earns compound interest, both for 2 years. If the difference in their final amounts is ₹100, what is Sum A (assuming both principals are equal)?

Accepted Answer

Step 1: Let principal = P. After 2 years with SI: Amount_A = P + (P × 10 × 2)/100 = P + 0.2P = 1.2P. Step 2: After 2 years with CI: Amount_B = P(1.10)² = 1.21P. Step 3: Difference = Amount_B - Amount_A = 1.21P - 1.2P = 0.01P = 100. Step 4: P = 10,000. Therefore, Sum A (principal) = ₹10,000.

Question 9

A sum of ₹6,000 is invested at a certain rate per annum. The compound interest for 2 years is ₹1,260 and the simple interest for the same period is ₹1,200. What is the rate of interest?

Accepted Answer

Step 1: From SI formula: SI = (P × R × T) / 100 → 1200 = (6000 × R × 2) / 100 → 1200 = 120R → R = 10% per annum. Step 2: Verify with CI: A = P(1 + R/100)^T = 6000(1.10)² = 6000 × 1.21 = 7260. CI = 7260 - 6000 = 1260. ✓ Confirmed.

Question 10

The simple interest on a sum for 2 years at 9% per annum is ₹900. If the same sum is invested at the same rate for the same period at compound interest, what will be the difference between the compound interest and simple interest?

Accepted Answer

Step 1: From SI formula, find principal: SI = (P × R × T) / 100 → 900 = (P × 9 × 2) / 100 → 900 = 18P → P = 50. Step 2: Calculate CI: A = P(1 + R/100)^T = 50(1.09)² = 50 × 1.1881 = 59.405. CI = 59.405 - 50 = 9.405. Step 3: Difference = CI - SI = 9.405 - 9 = 0.405. Wait, recalculate: P = 900 × 100 / (9 × 2) = 90000 / 18 = 5000. Step 2 (revised): A = 5000(1.09)² = 5000 × 1.1881 = 5940.5. CI = 5940.5 - 5000 = 940.5. Step 3: Difference = 940.5 - 900 = 40.5.

Question 11

A principal amount becomes ₹14,520 in 2 years at 10% per annum under compound interest. What would be the difference between CI and SI if the same principal is invested for 3 years at the same rate?

Accepted Answer

Step 1: A = P(1.10)² = 14,520 ⟹ P × 1.21 = 14,520 ⟹ P = 12,000. Step 2: For 3 years at 10%, SI = (12,000 × 10 × 3)/100 = 3,600. Step 3: CI = 12,000[(1.10)³ - 1] = 12,000[1.331 - 1] = 12,000 × 0.331 = 3,972. Step 4: Difference = 3,972 - 3,600 = 372. Therefore, the difference is ₹372.

Question 12

The difference between CI and SI on a sum for 2 years at r% per annum is ₹100. If the rate is increased by 2%, the difference becomes ₹144. Find the rate of interest.

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 10,000. So, 100 = P × r² / 10,000 ⟹ P × r² = 1,000,000. Step 2: At (r+2)%: 144 = P × (r+2)² / 10,000 ⟹ P × (r+2)² = 1,440,000. Step 3: Dividing: (r+2)² / r² = 1.44 ⟹ (r+2) / r = 1.2 ⟹ r + 2 = 1.2r ⟹ 0.2r = 2 ⟹ r = 10. Therefore, the rate is 10% per annum.

Question 13

A principal becomes ₹19,360 after 2 years at 10% per annum under compound interest. If the same principal is invested at 12% per annum for 2 years, what is the difference between the CI and SI at the new rate?

Accepted Answer

Step 1: A = P(1.10)² = 19,360 ⟹ P × 1.21 = 19,360 ⟹ P = 16,000. Step 2: At 12% for 2 years, SI = (16,000 × 12 × 2) / 100 = 3,840. Step 3: CI = 16,000 × [(1.12)² - 1] = 16,000 × [1.2544 - 1] = 16,000 × 0.2544 = 4,070.40. Step 4: Difference = 4,070.40 - 3,840 = 230.40. Therefore, the difference is ₹230.40.

Question 14

The difference between CI and SI on a certain sum for 2 years at 10% per annum is ₹40. If the same sum is invested at 15% per annum for 2 years, what will be the difference between CI and SI?

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 10,000. At 10%: 40 = P × 100 / 10,000 ⟹ P = 4,000. Step 2: At 15% for 2 years: Difference = 4,000 × 225 / 10,000 = 90. Therefore, the difference is ₹90.

SBI PO Difference SI vs CI

SBI PO Difference SI vs CI — Past Exam Questions

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60-Second Revision — Difference SI vs CI