Simple Interest – Solved Problems with Explanation
Simple Interest is a fundamental topic in arithmetic and finance. It is widely used in banking, loans, savings, and competitive examinations. Understanding this concept helps in solving real-life money-related problems.
In this article, we will solve multiple Simple Interest problems step by step using clear formulas and logical reasoning.
Simple Interest Formula
Simple Interest (SI) = (Principal × Rate × Time) ÷ 100
- Principal (P): Original amount of money
- Rate (R): Rate of interest per annum
- Time (T): Time in years
Solved Simple Interest Problems
Problem 1: Find the simple interest on ₹5,000 at 10% per annum for 2 years.
Solution:
P = ₹5,000 R = 10% T = 2 years
SI = (5000 × 10 × 2) ÷ 100 = ₹1,000
Simple Interest = ₹1,000
Problem 2: Find the amount after 3 years if ₹8,000 is invested at 5% per annum.
Solution:
SI = (8000 × 5 × 3) ÷ 100 = ₹1,200
Amount = Principal + Interest = 8000 + 1200 = ₹9,200
Amount = ₹9,200
Problem 3: Calculate the simple interest on ₹12,000 for 1.5 years at 8% per annum.
Solution:
P = ₹12,000 R = 8% T = 1.5 years
SI = (12000 × 8 × 1.5) ÷ 100 = ₹1,440
Simple Interest = ₹1,440
Problem 4: If the simple interest on a sum for 4 years at 6% is ₹2,400, find the principal.
Solution:
SI = ₹2,400 R = 6% T = 4 years
P = (SI × 100) ÷ (R × T) = (2400 × 100) ÷ (6 × 4) = ₹10,000
Principal = ₹10,000
Problem 5: At what rate will ₹7,500 earn ₹1,125 as simple interest in 3 years?
Solution:
P = ₹7,500 SI = ₹1,125 T = 3 years
R = (SI × 100) ÷ (P × T) = (1125 × 100) ÷ (7500 × 3) = 5%
Rate = 5% per annum
Problem 6: In how many years will ₹6,000 earn ₹1,800 at 10% simple interest?
Solution:
P = ₹6,000 SI = ₹1,800 R = 10%
T = (SI × 100) ÷ (P × R) = (1800 × 100) ÷ (6000 × 10) = 3 years
Time = 3 years
Problem 7: Find the interest earned if ₹9,000 is invested for 2 years at 7.5% per annum.
Solution:
SI = (9000 × 7.5 × 2) ÷ 100 = ₹1,350
Interest = ₹1,350
Problem 8: A sum amounts to ₹11,500 in 5 years at 6% simple interest. Find the principal.
Solution:
Let Principal = P
SI = (P × 6 × 5) ÷ 100 = 0.3P
Amount = P + SI = 1.3P
1.3P = 11,500 P = ₹8,846 (approx.)
Principal ≈ ₹8,846
Exam Tips
✔ Always convert months into years
✔ Use formula rearrangement for unknown values
✔ Write all given values clearly before solving
Common Mistakes
- Not converting time correctly
- Incorrect substitution in formula
- Forgetting to divide by 100
- Mixing simple interest with compound interest
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