चक्रवृद्धि ब्याज (Compound Interest): प्रतियोगी परीक्षाओं के लिए महत्वपूर्ण सूत्र और ट्रिक्स

Q1. A sum of money doubles itself in 10 years at compound interest. In how many years will it become 8 times itself?

1. 20 years
2. 30 years
3. 40 years
4. 25 years

Explanation: If a sum becomes 2 times in 't' years, it will become 2^n times in n*t years. Here, the sum doubles (2 times) in 10 years. To become 8 times (which is 2^3), it will take 3 * 10 = 30 years.

Q2. What is the compound interest on Rs. 10,000 for 2 years at 4% per annum, compounded annually?

1. Rs. 800
2. Rs. 816
3. Rs. 832
4. Rs. 824

Explanation: Principal (P) = Rs. 10,000, Rate (r) = 4%, Time (t) = 2 years. Amount (A) = P(1 + r/100)^t = 10000(1 + 4/100)^2 = 10000(1.04)^2 = 10000 * 1.0816 = Rs. 10,816. Compound Interest (CI) = A - P = 10816 - 10000 = Rs. 816.

Q3. The difference between the compound interest and simple interest on a certain sum for 2 years at 5% per annum is Rs. 25. What is the sum?

1. Rs. 8,000
2. Rs. 10,000
3. Rs. 9,000
4. Rs. 12,000

Explanation: The formula for the difference between CI and SI for 2 years is CI - SI = P(r/100)^2. We are given CI - SI = Rs. 25 and r = 5%. So, 25 = P(5/100)^2 = P(1/20)^2 = P/400. Therefore, P = 25 * 400 = Rs. 10,000. Wait, let me recheck the calculation. 25 = P(5/100)^2 = P(0.05)^2 = P(0.0025). P = 25 / 0.0025 = 25 / (25/10000) = 25 * (10000/25) = 10000. Oops, the options seem incorrect based on my calculation. Let me re-evaluate the options and calculation. Ah, the difference is Rs. 25. P(5/100)^2 = 25 => P(1/20)^2 = 25 => P/400 = 25 => P = 25 * 400 = 10000. Let me check the options again. It seems there might be a typo in the question or options provided. However, if we assume the difference was Rs. 100, then P(5/100)^2 = 100 => P/400 = 100 => P = 40000. If the difference was Rs. 40, then P/400 = 40 => P = 16000. Let's assume the question meant Rs. 100 difference. If the difference is Rs. 25, and rate is 5%, P = 10000. Let's re-examine the options. If P = 8000, difference = 8000 * (5/100)^2 = 8000 * (1/20)^2 = 8000/400 = 20. If P = 10000, difference = 10000 * (5/100)^2 = 10000/400 = 25. So, the sum is Rs. 10,000. The correct option is 10,000. My initial calculation was correct, and option B is the correct answer.

Q4. On what sum of money will the compound interest for 3 years at 10% per annum be Rs. 331 more than the simple interest for the same period?

1. Rs. 1,000
2. Rs. 10,000
3. Rs. 5,000
4. Rs. 2,000

Explanation: The difference between CI and SI for 3 years is given by CI - SI = P(r/100)^2 * (300 + r)/100. We are given CI - SI = Rs. 331 and r = 10%. So, 331 = P(10/100)^2 * (300 + 10)/100 = P(1/10)^2 * (310/100) = P(1/100) * (31/10) = P * 31 / 1000. Therefore, P = (331 * 1000) / 31 = 10 * 1000 = Rs. 10,000.

Q5. A sum of money is invested at compound interest. If it doubles in 5 years, how many years will it take for the sum to become 16 times the original amount?

1. 15 years
2. 20 years
3. 25 years
4. 30 years

Explanation: If a sum doubles (becomes 2 times) in 5 years, it will become 2^n times in n*5 years. We want to find the time it takes to become 16 times. Since 16 = 2^4, we need n=4. Therefore, the time required is 4 * 5 = 20 years.