Difficulty: Easy
Correct Answer: 2 years
Explanation:
Introduction:
This problem checks whether you can use the basic compound interest formula to relate principal, rate, time and interest. We know the principal, the rate and the total compound interest earned, and we must determine the number of years the money was invested.
Given Data / Assumptions:
Concept / Approach:
The compound interest formula for amount is A = P * (1 + r/100)^n. The compound interest earned is CI = A - P. By substituting the known values and trying integer values of n, we can find which year count gives the required interest of Rs 4347.
Step-by-Step Solution:
Let n be the number of years.A = P * (1 + 7/100)^n = 30000 * (1.07)^nCI = A - P = 30000 * (1.07)^n - 30000We need CI = 4347, so 30000 * (1.07)^n - 30000 = 4347Try n = 2: A2 = 30000 * (1.07)^2 = 30000 * 1.1449 = Rs 34347CI for 2 years = 34347 - 30000 = Rs 4347, which matches the given interest.Hence, n = 2 years.
Verification / Alternative Check:
You can also test n = 1 and n = 3 to ensure they do not work. For 1 year, CI = 30000 * 0.07 = Rs 2100 (too low). For 3 years, CI would be even higher than Rs 4347. Therefore, only n = 2 years satisfies the condition.
Why Other Options Are Wrong:
2.5 years and 3 years: These would give an amount larger than Rs 34347 and hence a greater CI.4 years: Gives an even larger compound interest, so it cannot be correct.1 year: Produces only Rs 2100 as interest, which is much less than Rs 4347.
Common Pitfalls:
Many learners forget that time in the standard formula is usually taken as an integer number of compounding periods unless a fractional period is clearly specified. Some also mistakenly equate CI directly to P * r/100 * n, which is the simple interest formula, not the compound interest formula.
Final Answer:
The money was invested for 2 years to earn compound interest of Rs 4347 at 7% per annum on Rs 30000.
Discussion & Comments