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

The difference between compound interest and simple interest on ₹4,000 for 2 years is ₹40. What is the rate of interest per annum?

Accepted Answer

Step 1: Use the formula for 2 years: CI - SI = P × R² / (100)². Step 2: Substitute: 40 = 4000 × R² / 10000. Step 3: Simplify: 40 = 4R² / 10 = 0.4R². Step 4: Solve: R² = 40 / 0.4 = 100, so R = 10% per annum.

Question 3

A sum of ₹6,000 is invested at 15% per annum. The simple interest for 1 year is ₹900. If the same sum is invested at compound interest for 1 year at the same rate, what is the difference between CI and SI?

Accepted Answer

Step 1: For 1 year, compound interest and simple interest are always equal because there is no compounding effect in the first year. Step 2: CI for 1 year = A - P = 6000(1.15) - 6000 = 6900 - 6000 = ₹900. Step 3: SI for 1 year = ₹900 (given). Step 4: Difference = 900 - 900 = ₹0.

Question 4

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

Question 5

A principal amount earns ₹400 as simple interest in 2 years at 8% per annum. If the same principal is invested at 8% compound interest for 2 years, how much more interest will be earned?

Accepted Answer

Step 1: Find principal from SI formula: SI = (P × R × T) / 100, so 400 = (P × 8 × 2) / 100, thus P = 400 × 100 / 16 = ₹2,500. Step 2: Calculate CI: A = 2500(1.08)² = 2500 × 1.1664 = ₹2,916. Step 3: CI = 2916 - 2500 = ₹416. Step 4: Additional interest = CI - SI = 416 - 400 = ₹16.

Question 6

₹8,000 is lent at 5% per annum compound interest. The difference between CI and SI for 3 years is ₹61. What is the compound interest for 3 years?

Accepted Answer

Step 1: Use the formula for difference: CI - SI = P × R² × (R + 300) / (100)³ for 3 years, or calculate directly. Step 2: SI = (8000 × 5 × 3) / 100 = ₹1,200. Step 3: A = 8000(1.05)³ = 8000 × 1.157625 = ₹9,261. Step 4: CI = 9261 - 8000 = ₹1,261. Step 5: Verify difference: 1261 - 1200 = ₹61 ✓

Question 7

The difference between compound interest and simple interest on a sum for 3 years at 8% per annum is ₹245.76. Find the principal.

Accepted Answer

Step 1: Use the formula for difference: CI − SI = P × R² × (300 + R) / 100³ for 3 years. Alternatively, compute directly: Let P be principal. SI = (P × 8 × 3) / 100 = 0.24P. For CI: A = P(1.08)³ = P × 1.259712. CI = P(1.259712 − 1) = 0.259712P. Step 2: Difference = 0.259712P − 0.24P = 0.019712P = 245.76. Step 3: P = 245.76 / 0.019712 = ₹12,500.

Question 8

A principal amount earns ₹500 as simple interest in 2 years at 5% per annum. If the same principal is invested at 5% compound interest for 2 years, what is the compound interest earned?

Accepted Answer

Step 1: Find Principal from SI formula: SI = (P × R × T) / 100 ⟹ 500 = (P × 5 × 2) / 100 ⟹ P = ₹5,000. Step 2: Calculate CI: A = P(1 + R/100)^T = 5000(1.05)^2 = 5000 × 1.1025 = ₹5,512.50. Step 3: CI = 5,512.50 − 5,000 = ₹512.50.

Question 9

A sum becomes ₹1,210 in 2 years and ₹1,331 in 3 years under compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Let principal = P and rate = R% p.a. From the given data: P(1 + R/100)² = 1,210 and P(1 + R/100)³ = 1,331. Step 2: Divide the second equation by the first: [P(1 + R/100)³] / [P(1 + R/100)²] = 1,331 / 1,210 ⟹ (1 + R/100) = 1.1 ⟹ R/100 = 0.1 ⟹ R = 10%. Step 3: Verify: P(1.1)² = 1,210 ⟹ P = 1,000. Check: 1,000(1.1)³ = 1,331 ✓

Question 10

A person invests ₹6,400 at 12.5% per annum compound interest. After how many years will the amount become ₹10,240?

Accepted Answer

Step 1: Use A = P(1 + R/100)^T. Here, 10,240 = 6,400(1 + 12.5/100)^T ⟹ 10,240 = 6,400(1.125)^T. Step 2: Simplify: 10,240 / 6,400 = (1.125)^T ⟹ 1.6 = (1.125)^T. Step 3: Note that 1.125 = 9/8. So (9/8)^T = 1.6 = 8/5. Step 4: (9/8)^T = 8/5. Testing T = 2: (9/8)² = 81/64 ≈ 1.266 (too small). Testing T = 3: (9/8)³ = 729/512 ≈ 1.424 (close). Testing T = 4: (9/8)⁴ = 6561/4096 ≈ 1.601 ≈ 1.6 ✓. Therefore T = 4 years.

Question 11

A sum of ₹8,000 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: SI = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Calculate Compound Interest: A = P(1 + R/100)^T = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. CI = 9,680 − 8,000 = ₹1,680. Step 3: Difference = CI − SI = 1,680 − 1,600 = ₹80.

Question 12

The simple interest on a sum for 2 years at 6% per annum is ₹480. If the same sum is invested at 6% compound interest for 2 years, how much more interest will be earned compared to simple interest?

Accepted Answer

Step 1: Find principal from SI: SI = (P × R × T) / 100 ⟹ 480 = (P × 6 × 2) / 100 ⟹ P = ₹4,000. Step 2: Calculate CI: A = P(1 + R/100)^T = 4,000(1.06)² = 4,000 × 1.1236 = ₹4,494.40. CI = 4,494.40 − 4,000 = ₹494.40. Step 3: Difference = CI − SI = 494.40 − 480 = ₹14.40.

Question 13

A principal amount is invested at 8% per annum. The difference between compound interest for 2 years and simple interest for 2 years is ₹51.20. If the same principal is invested at 6% per annum for 3 years under compound interest, what will be the compound interest earned?

Accepted Answer

Step 1: Find principal using CI - SI difference for 2 years. For 2 years: CI - SI = P × r² / 10000. So 51.20 = P × 64 / 10000. Therefore P = (51.20 × 10000) / 64 = ₹8,000. Step 2: Now calculate CI at 6% for 3 years: A = P(1 + r/100)³ = 8000(1.06)³ = 8000 × 1.191016 = ₹9,528.128 ≈ ₹9,528.13. Step 3: CI = A - P = 9528.13 - 8000 = ₹1,528.13.

Question 14

Two equal sums are invested at the same rate of interest per annum for 2 years. One sum is invested under simple interest and the other under compound interest. If the difference between the amounts received is ₹40, and the rate of interest is 10% per annum, what is each sum?

Accepted Answer

Step 1: Let the principal be P. For 2 years at 10% per annum: SI = (P × 10 × 2) / 100 = 0.2P. Amount under SI = P + 0.2P = 1.2P. Step 2: Amount under CI = P(1.1)² = 1.21P. Step 3: Difference = 1.21P - 1.2P = 0.01P = 40. Step 4: P = 40 / 0.01 = ₹4,000.

Question 15

The compound interest on a sum for 2 years at 10% per annum exceeds the simple interest on the same sum for the same period and rate by ₹100. What is the principal? Additionally, if this principal is invested at 12% per annum compound interest for 2 years, what will be the total amount?

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 10000 = P × 100 / 10000 = P / 100. Given this equals ₹100, so P / 100 = 100, therefore P = ₹10,000. Step 2: Now calculate amount at 12% for 2 years: A = P(1 + r/100)² = 10000(1.12)² = 10000 × 1.2544 = ₹12,544.

Question 16

A sum of money becomes ₹4,840 in 2 years at 10% per annum under simple interest. What will be the difference between compound interest and simple interest on the same principal for the same period and rate?

Accepted Answer

Step 1: Find principal using SI formula. Amount = P + SI, where SI = (P × R × T)/100. So 4840 = P + (P × 10 × 2)/100 = P + 0.2P = 1.2P. Therefore P = 4840/1.2 = ₹4,000. Step 2: Calculate SI for 2 years = (4000 × 10 × 2)/100 = ₹800. Step 3: Calculate CI using A = P(1 + r/100)^t = 4000(1.1)^2 = 4000 × 1.21 = ₹4,840. So CI = 4840 - 4000 = ₹840. Step 4: Difference = CI - SI = 840 - 800 = ₹40.

SSC MTS Difference SI vs CI

SSC MTS Difference SI vs CI — Past Exam Questions

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60-Second Revision — Difference SI vs CI