Multiple choice

What will be the compound interest earned on an amount of $Rs. 5000$ in $2$ years? I. The simple interest on the same amount at the same rate of interest in $5$ years is $Rs. 2000$. II. The compound interest and the simple interest earned in one year is the same. III. The amount becomed more than double on compound interest in $10$ years.

  1. I only

  2. I and II only

  3. II and III only

  4. I and III only

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: SI = 2000 for 5 years at 5000 principal means SI = 400 per year. Rate = (400/5000)*100 = 8%. With rate and principal, CI for 2 years can be calculated. Statement II: CI and SI are same for 1 year, which is always true for any rate, so it provides no info. Statement III: Amount > double in 10 years gives a range for the rate, but not a specific value. Thus, only I is sufficient.

AI explanation

Statement I provides the simple interest for 5 years as Rs. 2000 on a principal of Rs. 5000, allowing you to find the rate using the simple interest formula: R equals (2000 multiplied by 100) divided by (5000 multiplied by 5), resulting in an 8 percent interest rate. Using this rate in the compound interest formula, the compound interest for 2 years can be calculated as 5000 multiplied by the quantity (1.08 squared minus 1), yielding Rs. 832. Statement II is a known fact that does not provide the rate, and Statement III lacks specific values to determine the exact rate, so only statement I is sufficient. The result is I only.

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