Question 1

At what rate per annum will the difference between compound interest and simple interest on ₹8,000 for 2 years be ₹80?

Accepted Answer

Step 1: For 2 years, the difference formula is: Difference = P × R² / (100)² = (P × R²) / 10000. Step 2: Substitute values: 80 = (8000 × R²) / 10000. Step 3: 80 = 0.8 × R². Step 4: R² = 100, so R = 10% per annum.

Question 2

A principal of ₹10,000 is invested at 5% per annum. The difference between compound interest and simple interest for 3 years is ₹76.25. Which of the following is closest to this difference?

Accepted Answer

Step 1: Calculate SI = (10000 × 5 × 3) / 100 = ₹1,500. Step 2: Calculate Amount for CI: A = 10000(1.05)³ = 10000 × 1.157625 = ₹11,576.25. Step 3: CI = 11576.25 - 10000 = ₹1,576.25. Step 4: Difference = 1576.25 - 1500 = ₹76.25.

Question 3

A sum becomes ₹12,100 in 2 years at 10% per annum under compound interest. What would be the simple interest on the same sum for the same period at the same rate?

Accepted Answer

Step 1: Find Principal using A = P(1 + R/100)^T: 12100 = P(1.1)². Step 2: 12100 = P × 1.21, so P = ₹10,000. Step 3: Calculate SI = (10000 × 10 × 2) / 100 = ₹2,000.

Question 4

The simple interest on a sum for 2 years at 8% per annum is ₹1,600. What will be the compound interest on the same sum at the same rate for the same period?

Accepted Answer

Step 1: From SI formula, find Principal: SI = (P × R × T) / 100, so 1600 = (P × 8 × 2) / 100. Step 2: 1600 = 16P/100, so P = ₹10,000. Step 3: Calculate CI: A = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. Step 4: CI = 11664 - 10000 = ₹1,664.

Question 5

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

Accepted Answer

Step 1: For 2 years, CI - SI = (P × R²) / (100)². Step 2: 144 = (P × 144) / 10000. Step 3: 144 × 10000 = P × 144. Step 4: P = 10000.

Question 6

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 7

A principal amount becomes ₹12,100 in 2 years at 10% per annum under compound interest. What would be the simple interest earned on the same principal for the same period and rate?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T: 12,100 = P(1.10)^2 = P × 1.21, so P = 10,000. Step 2: Calculate SI: SI = (10,000 × 10 × 2) / 100 = ₹2,000.

Question 8

The compound interest on ₹6,000 at 5% per annum for 2 years is how much more than the simple interest on the same principal at the same rate and time?

Accepted Answer

Step 1: Calculate SI: SI = (6,000 × 5 × 2) / 100 = ₹600. Step 2: Calculate CI: A = 6,000(1.05)^2 = 6,000 × 1.1025 = ₹6,615. CI = 6,615 - 6,000 = ₹615. Step 3: Difference = CI - SI = 615 - 600 = ₹15.

Question 9

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

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% p.a. Step 2: For the sum to triple, SI = 2P. Using 2P = (P × 20 × T) / 100: 2P = 0.2PT, so T = 10 years.

Question 10

At what rate 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, Difference = P × R² / 10,000. Step 2: Substitute: 50 = 5,000 × R² / 10,000 = R² / 2. Step 3: R² = 100, so R = 10% per annum.

Question 11

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 12

The compound interest on a sum for 2 years at 5% p.a. is ₹410. What is the difference between the compound interest and simple interest on the same sum for the same period and rate?

Accepted Answer

Step 1: For CI, CI = P[(1 + r/100)ⁿ – 1]. So 410 = P[(1.05)² – 1] = P[1.1025 – 1] = 0.1025P. Step 2: P = 410 / 0.1025 = 4,000. Step 3: For SI, SI = (P × R × T) / 100 = (4,000 × 5 × 2) / 100 = 400. Step 4: Difference = CI – SI = 410 – 400 = ₹10. Therefore, the difference is ₹10.

Question 13

A sum becomes ₹8,800 in 2 years and ₹9,680 in 3 years under compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: The amount grows from ₹8,800 (at 2 years) to ₹9,680 (at 3 years). Step 2: Interest earned in the 3rd year = 9,680 – 8,800 = ₹880. Step 3: This ₹880 is interest on ₹8,800 for 1 year. Step 4: Rate = (880 / 8,800) × 100 = 10% per annum. Therefore, the rate is 10% p.a.

Question 14

The simple interest on a sum for 4 years at 8% p.a. is ₹3,200. If the same sum is invested at 8% p.a. compound interest for 2 years, what will be the compound interest earned?

Accepted Answer

Step 1: From SI formula, SI = (P × R × T) / 100. So 3,200 = (P × 8 × 4) / 100. Step 2: 3,200 = 32P / 100, thus P = 10,000. Step 3: For CI at 8% p.a. for 2 years: Amount = P(1 + r/100)² = 10,000(1.08)² = 10,000 × 1.1664 = 11,664. Step 4: CI = 11,664 – 10,000 = ₹1,664. Therefore, compound interest is ₹1,664.

Question 15

The difference between CI and SI on a certain sum for 2 years at 12% per annum is ₹432. If the same sum is invested at 12% p.a. simple interest for 3 years, what will be the simple interest?

Accepted Answer

Step 1: For 2 years, CI – SI = P × r² / 10,000. So 432 = P × 144 / 10,000. Step 2: P = (432 × 10,000) / 144 = 30,000. Step 3: SI for 3 years at 12% p.a. = (P × R × T) / 100 = (30,000 × 12 × 3) / 100 = 10,800. Therefore, simple interest is ₹10,800.

Question 16

A principal amount becomes ₹12,100 under compound interest at 10% p.a. for 2 years. If the same principal is invested at simple interest for 3 years at the same rate, what will be the amount?

Accepted Answer

Step 1: For CI, A = P(1 + r/100)ⁿ. So 12,100 = P(1.10)². Step 2: 12,100 = P × 1.21, thus P = 10,000. Step 3: For SI for 3 years at 10% p.a.: SI = (10,000 × 10 × 3) / 100 = 3,000. Step 4: Amount = P + SI = 10,000 + 3,000 = 13,000. Therefore, the amount is ₹13,000.

SSC GD Constable Difference SI vs CI

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