Question 1

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

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

A principal of ₹10,000 is invested at 8% per annum. The difference between CI and SI for 3 years is:

Accepted Answer

Step 1: SI = (10000 × 8 × 3) / 100 = ₹2,400. Step 2: CI = 10000(1.08)^3 - 10000. Calculate (1.08)^3 = 1.259712, so A = 10000 × 1.259712 = 12,597.12, thus CI = 12597.12 - 10000 = ₹2,597.12. Step 3: Difference = 2597.12 - 2400 = ₹197.12 ≈ ₹197.

Question 3

If the difference between CI and SI on a sum at 12% per annum for 2 years is ₹144, what is the principal?

Accepted Answer

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

Question 4

A principal amount becomes ₹11,664 after 2 years at 8% per annum compound interest. What would be the simple interest earned on the same principal for the same period at the same rate?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T: 11,664 = P(1.08)^2 = P × 1.1664. Step 2: P = 11,664 / 1.1664 = ₹10,000. Step 3: Calculate SI = (P × R × T) / 100 = (10,000 × 8 × 2) / 100 = ₹1,600.

Question 5

At what rate of interest per annum will the difference between compound interest and simple interest on ₹5,000 for 2 years be ₹50?

Accepted Answer

Step 1: For 2 years, CI - SI = P × R² / (100)². Step 2: 50 = 5000 × R² / 10000 = R² / 2. Step 3: R² = 100, so R = 10% per annum.

Question 6

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 7

A sum of money doubles itself in 5 years at simple interest. In how many years will it triple itself at the same rate of interest?

Accepted Answer

Step 1: If principal is P and it doubles in 5 years, then SI = P. Using SI = (P × R × T) / 100: P = (P × R × 5) / 100, so R = 20% per annum. Step 2: For the sum to triple, SI needed = 2P. Using 2P = (P × 20 × T) / 100, we get 2P = 0.2PT, so T = 10 years.

Question 8

The compound interest on ₹4,000 for 2 years is ₹410. What is the rate of interest per annum, and what would be the simple interest for the same principal and period?

Accepted Answer

Step 1: CI = A - P, so 410 = A - 4000, giving A = ₹4,410. Step 2: Using A = P(1 + R/100)^T: 4410 = 4000(1 + R/100)². Step 3: (1 + R/100)² = 1.1025, so 1 + R/100 = 1.05, giving R = 5% per annum. Step 4: SI = (4000 × 5 × 2) / 100 = ₹400.

Question 9

A principal amount becomes ₹6,050 in 2 years at 10% per annum under compound interest. What would be the simple interest on the same principal for the same period and rate?

Accepted Answer

Step 1: Amount = P(1 + r/100)ⁿ. So 6,050 = P(1.1)². Step 2: 6,050 = P × 1.21, so P = 6,050 ÷ 1.21 = 5,000. Step 3: SI = (P × r × t)/100 = (5,000 × 10 × 2)/100 = 1,000.

Question 10

The difference between the compound interest and simple interest on a sum for 2 years at 8% per annum is ₹64. If the same sum is invested for 4 years at the same rate, what is the difference between CI and SI?

Accepted Answer

Step 1: For 2 years at 8%, CI - SI = P×r²/10000 = P×64/10000 = 0.0064P. Given: 0.0064P = 64, so P = 10,000. Step 2: For 4 years, SI = (10,000 × 8 × 4)/100 = 3,200. Step 3: CI = 10,000[(1.08)⁴ - 1]. Calculate (1.08)⁴ = 1.3605 (approx), so CI = 10,000 × 0.3605 = 3,605. Step 4: Difference = 3,605 - 3,200 = 405.

Question 11

A sum of ₹8,000 is invested at a certain rate per annum. After 2 years, the compound interest exceeds the simple interest by ₹80. What is the rate of interest per annum?

Accepted Answer

Step 1: CI - SI for 2 years = P×r²/10000. So 80 = 8,000×r²/10000 = 0.8r². Step 2: r² = 80/0.8 = 100, so r = 10% per annum.

SSC CPO Difference SI vs CI

Difference SI vs CI— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Difference SI vs CI — Practice Questions

60-Second Revision — Difference SI vs CI