Difficulty: Easy
Correct Answer: 3 years
Explanation:
Introduction:
This question asks you to find the time needed for a given principal to grow to a specified amount under compound interest. It is a straightforward application of the compound interest amount formula, solved for the time period when rate and amounts are known.
Given Data / Assumptions:
Concept / Approach:
For annual compounding, the amount is given by A = P * (1 + r/100)^t. We plug in the known values of A, P and r, and then solve for t. In many exam problems like this, the numbers are chosen so that (1 + r/100)^t becomes a familiar power such as 1.1^3, making the solution simple without logarithms.
Step-by-Step Solution:
Formula: A = P * (1 + r/100)^tSubstitute: 1331 = 1000 * (1 + 10/100)^t = 1000 * (1.1)^tSo (1.1)^t = 1331 / 1000 = 1.331Recall that 1.1^3 = 1.331 (since 11^3 = 1331).Therefore, (1.1)^t = (1.1)^3, which implies t = 3.
Verification / Alternative Check:
You can compute the amount year by year. After 1 year: 1000 * 1.1 = 1100. After 2 years: 1100 * 1.1 = 1210. After 3 years: 1210 * 1.1 = 1331. This confirms that it takes exactly 3 years to reach Rs 1331 at 10% compound interest.
Why Other Options Are Wrong:
2 years: Gives 1000 * 1.1^2 = Rs 1210, which is less than 1331.4 years: Gives 1000 * 1.1^4 = Rs 1464.10, which is more than 1331.5 years and 6 years: Produce even larger amounts and therefore cannot be correct.
Common Pitfalls:
Some students try to apply the simple interest formula or linearly scale the interest, which is not appropriate for compound interest. Others may struggle with solving for t algebraically, but recognizing common powers of 1.1 or 1.05 can greatly simplify such questions in competitive exams.
Final Answer:
The required time for Rs 1000 to amount to Rs 1331 at 10% compound interest is 3 years.
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