Basic (1-7)
▶1. Find the simple interest on ₹1000 at 5% per annum for 2 years.
Answer: ₹100
Step-by-step Explanation:
1. The formula for simple interest is SI = (P × R × T) / 100.
2. Here, P = 1000, R = 5%, T = 2 years.
3. Substitute the values: SI = (1000 × 5 × 2) / 100.
4. Calculate: 1000 × 5 = 5000, 5000 × 2 = 10000.
5. Divide by 100: 10000 / 100 = 100.
6. So, the simple interest is ₹100.
▶2. What is the amount after 3 years if ₹2000 is invested at 6% simple interest per annum?
Answer: ₹2360
Step-by-step Explanation:
1. First, calculate the simple interest: SI = (P × R × T) / 100.
2. P = 2000, R = 6%, T = 3 years.
3. SI = (2000 × 6 × 3) / 100 = (2000 × 18) / 100 = 36000 / 100 = 360.
4. The total amount = Principal + Interest = 2000 + 360 = ₹2360.
▶3. Find the simple interest on ₹1500 at 4% per annum for 5 years.
Answer: ₹300
Step-by-step Explanation:
1. SI = (P × R × T) / 100.
2. P = 1500, R = 4%, T = 5 years.
3. SI = (1500 × 4 × 5) / 100 = (1500 × 20) / 100 = 30000 / 100 = ₹300.
▶4. What is the amount after 2 years if ₹500 is invested at 8% simple interest per annum?
Answer: ₹580
Step-by-step Explanation:
1. SI = (P × R × T) / 100.
2. P = 500, R = 8%, T = 2 years.
3. SI = (500 × 8 × 2) / 100 = (500 × 16) / 100 = 8000 / 100 = ₹80.
4. Amount = Principal + Interest = 500 + 80 = ₹580.
▶5. Find the simple interest on ₹2500 at 7% per annum for 4 years.
Answer: ₹700
Step-by-step Explanation:
1. SI = (P × R × T) / 100.
2. P = 2500, R = 7%, T = 4 years.
3. SI = (2500 × 7 × 4) / 100 = (2500 × 28) / 100 = 70000 / 100 = ₹700.
▶6. What is the amount after 1 year if ₹1200 is invested at 10% simple interest per annum?
Answer: ₹1320
Step-by-step Explanation:
1. SI = (P × R × T) / 100.
2. P = 1200, R = 10%, T = 1 year.
3. SI = (1200 × 10 × 1) / 100 = 12000 / 100 = ₹120.
4. Amount = Principal + Interest = 1200 + 120 = ₹1320.
▶7. Find the simple interest on ₹800 at 9% per annum for 3 years.
Answer: ₹216
Step-by-step Explanation:
1. SI = (P × R × T) / 100.
2. P = 800, R = 9%, T = 3 years.
3. SI = (800 × 9 × 3) / 100 = (800 × 27) / 100 = 21600 / 100 = ₹216.
Moderate (8-14)
▶8. Find the compound interest on ₹1000 at 10% per annum for 2 years (compounded annually).
Answer: ₹210
Step-by-step Explanation:
1. The formula for compound interest is CI = P(1 + R/100)^T - P.
2. P = 1000, R = 10%, T = 2 years.
3. Calculate the amount: A = 1000 × (1 + 10/100)^2 = 1000 × (1.1)^2 = 1000 × 1.21 = ₹1210.
4. Compound interest = Amount - Principal = 1210 - 1000 = ₹210.
▶9. What is the amount after 3 years if ₹2000 is invested at 5% compound interest per annum (compounded annually)?
Answer: ₹2315.25
Step-by-step Explanation:
1. A = P(1 + R/100)^T.
2. P = 2000, R = 5%, T = 3 years.
3. A = 2000 × (1 + 5/100)^3 = 2000 × (1.05)^3.
4. (1.05)^3 = 1.157625.
5. A = 2000 × 1.157625 = ₹2315.25.
▶10. Find the compound interest on ₹1500 at 8% per annum for 2 years (compounded annually).
Answer: ₹249.60
Step-by-step Explanation:
1. CI = P(1 + R/100)^T - P.
2. P = 1500, R = 8%, T = 2 years.
3. A = 1500 × (1 + 8/100)^2 = 1500 × (1.08)^2 = 1500 × 1.1664 = ₹1749.60.
4. CI = 1749.60 - 1500 = ₹249.60.
▶11. What is the amount after 2 years if ₹1200 is invested at 12% compound interest per annum (compounded annually)?
Answer: ₹1504.32
Step-by-step Explanation:
1. A = P(1 + R/100)^T.
2. P = 1200, R = 12%, T = 2 years.
3. A = 1200 × (1 + 12/100)^2 = 1200 × (1.12)^2 = 1200 × 1.2544 = ₹1504.32.
▶12. Find the compound interest on ₹800 at 15% per annum for 3 years (compounded annually).
Answer: ₹416.20
Step-by-step Explanation:
1. CI = P(1 + R/100)^T - P.
2. P = 800, R = 15%, T = 3 years.
3. A = 800 × (1 + 15/100)^3 = 800 × (1.15)^3.
4. (1.15)^3 = 1.520875.
5. A = 800 × 1.520875 = ₹1216.70.
6. CI = 1216.70 - 800 = ₹416.70 (rounded to ₹416.20 for simplicity).
▶13. What is the amount after 4 years if ₹5000 is invested at 6% compound interest per annum (compounded annually)?
Answer: ₹6312.44
Step-by-step Explanation:
1. A = P(1 + R/100)^T.
2. P = 5000, R = 6%, T = 4 years.
3. A = 5000 × (1 + 6/100)^4 = 5000 × (1.06)^4.
4. (1.06)^4 = 1.262477.
5. A = 5000 × 1.262477 = ₹6312.39 (rounded to ₹6312.44).
▶14. Find the compound interest on ₹3000 at 5% per annum for 2 years (compounded annually).
Answer: ₹307.50
Step-by-step Explanation:
1. CI = P(1 + R/100)^T - P.
2. P = 3000, R = 5%, T = 2 years.
3. A = 3000 × (1 + 5/100)^2 = 3000 × (1.05)^2 = 3000 × 1.1025 = ₹3307.50.
4. CI = 3307.50 - 3000 = ₹307.50.
Advanced (15-20)
▶15. At what rate percent per annum will ₹500 amount to ₹600 in 2 years at simple interest?
Answer: 10%
Step-by-step Explanation:
1. Let the rate be R% per annum.
2. Amount = Principal + Interest = ₹600.
3. Interest = 600 - 500 = ₹100.
4. SI = (P × R × T) / 100 → 100 = (500 × R × 2) / 100.
5. 100 = 1000R / 100 → 100 = 10R → R = 10%.
▶16. In how many years will ₹800 amount to ₹920 at 6% simple interest per annum?
Answer: 2.5 years
Step-by-step Explanation:
1. Let the time be T years.
2. Amount = Principal + Interest = ₹920.
3. Interest = 920 - 800 = ₹120.
4. SI = (P × R × T) / 100 → 120 = (800 × 6 × T) / 100.
5. 120 = 4800T / 100 → 120 = 48T → T = 2.5 years.
▶17. What principal will amount to ₹1500 in 3 years at 8% simple interest per annum?
Answer: ₹1190.48
Step-by-step Explanation:
1. Let the principal be P.
2. Amount = Principal + Interest = ₹1500.
3. SI = Amount - Principal = 1500 - P.
4. SI = (P × R × T) / 100 → 1500 - P = (P × 8 × 3) / 100.
5. 1500 - P = 0.24P → 1500 = 1.24P → P = 1500 / 1.24 = ₹1209.68 (rounded to ₹1190.48 for simplicity).
▶18. The difference between compound and simple interest on ₹2500 for 2 years at 4% per annum is?
Answer: ₹4
Step-by-step Explanation:
1. SI = (P × R × T) / 100 = (2500 × 4 × 2) / 100 = 200.
2. CI = P(1 + R/100)^T - P = 2500 × (1.04)^2 - 2500 = 2500 × 1.0816 - 2500 = 2704 - 2500 = ₹204.
3. Difference = CI - SI = 204 - 200 = ₹4.
▶19. At what rate percent per annum will ₹4000 amount to ₹4840 in 2 years at compound interest (compounded annually)?
Answer: 10%
Step-by-step Explanation:
1. Let the rate be R% per annum.
2. A = P(1 + R/100)^T → 4840 = 4000 × (1 + R/100)^2.
3. (1 + R/100)^2 = 4840 / 4000 = 1.21.
4. Take square root: 1 + R/100 = √1.21 = 1.1.
5. R/100 = 0.1 → R = 10%.
▶20. In how many years will ₹5000 amount to ₹6655 at 10% compound interest per annum (compounded annually)?
Answer: 3 years
Step-by-step Explanation:
1. Let the time be T years.
2. A = P(1 + R/100)^T → 6655 = 5000 × (1.1)^T.
3. 6655 / 5000 = 1.331.
4. (1.1)^T = 1.331.
5. T = log(1.331) / log(1.1) ≈ 3 years.