There is a 75 percent increase in an amount in 12.5 years at simple interest. What will be the compound interest on Rs. 20000 after 3 years at the same rate?

1. A

   Rs. 3820.32

2. B

   Rs. 3840.68

3. C

   Rs. 3720.32

4. D

   Rs. 3740.68

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

• The first step is to determine the annual interest rate using the simple interest formula. A 75% increase in 12.5 years means the rate is 75% / 12.5 years = 6% per year.
• The second step is to calculate the compound interest on Rs. 20,000 for 3 years at this 6% rate.
• Using the formula A = P(1 + R/100)ⁿ, the final amount is 20000 * (1.06)³ = Rs. 23,820.32.
• The compound interest is the final amount minus the initial principal: 23,820.32 - 20,000 = Rs. 3,820.32.

Why Other Options Were Wrong

• Option B: This value is incorrect. It likely arises from a miscalculation either in determining the rate or in applying the compound interest formula over three years.
• Option C: This value is incorrect. It is lower than the correct compound interest and may result from calculation errors or using an incorrect interest rate.
• Option D: This value is incorrect. It is a plausible-looking number but does not match the result of the correct compound interest calculation.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Simple and Compound Interest as background academic context rather than a clinical decision trigger.
• This is a non-nursing, quantitative aptitude question.
• Proficiency in mathematics, including topics like interest calculation, is essential for scoring well in the general aptitude sections of nursing recruitment and other competitive examinations.
• What if the interest was compounded semi-annually? The rate would be halved (3%) and the number of periods would be doubled (6). The calculation would be CI = 20000 * [(1.03)⁶ - 1], resulting in a different, slightly higher amount (Rs. 3852.55), as more frequent compounding yields more interest.

How to Approach the Question

• First, carefully read the question to identify that it has two parts: a simple interest scenario and a compound interest calculation.
• Use the information from the first part (75% increase in 12.5 years) to find the unknown variable, which is the annual interest rate.
• Remember the formula for simple interest rate: Rate = (Total Percentage Gain) / (Number of Years).
• Once the rate (6%) is found, apply it to the second part of the question.
• Use the standard formula for compound interest: CI = P * [(1 + R/100)ⁿ - 1].
• Calculate the value step-by-step to avoid errors and match the result with the given options.

Concept Tested & Keywords

• Concept Tested: Calculation of Simple and Compound Interest
• Stem keywords: simple interest, compound interest, 75 percent increase, 12.5 years, Rs. 20000, 3 years
• Lead-in keywords: What will be

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Q2SF94sLjhuz9qTp3Ym9St

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