What is the difference between simple interest and compound interest for 2 years on the sum of Rs. 1500 at 5% per annum?

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

the calculated difference between the Compound Interest (CI) and Simple Interest (SI) for the given parameters, which is Rs. 3.75.
First, calculate the Simple Interest (SI): SI = (1500 × 5 × 2) / 100 = Rs. 150.
Next, calculate the Compound Interest (CI). The amount after 2 years is A = 1500(1 + 5/100)² = Rs. 1653.75. So, CI = 1653.75 - 1500 = Rs. 153.75.
The difference is CI - SI = 153.75 - 150 = Rs. 3.75.
A shortcut formula for the difference over 2 years is P(R/100)², which also gives 1500 × (5/100)² = Rs. 3.75.

Option B: This value is an incorrect calculation. It does not match the result obtained from either the standard CI - SI method or the shortcut formula.
Option C: This value is an incorrect calculation. It does not match the result obtained from either the standard CI - SI method or the shortcut formula.
Option D: This value is an incorrect calculation. It does not match the result obtained from either the standard CI - SI method or the shortcut formula.

Visual 1: Flowchart: A side-by-side comparison of the calculation process for Simple Interest (SI) and Compound Interest (CI) for the given values, highlighting how CI includes interest on previously accrued interest.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Difference between Simple Interest and Compound Interest as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question testing mathematical skills, not a clinical concept.
While financial literacy is important for personal life, this specific calculation does not have a direct application in day-to-day clinical nursing duties.
What if? - If the stem changed one defining clue so that 3.75 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify the given values from the question: Principal (P) = Rs. 1500, Rate (R) = 5%, and Time (T) = 2 years.
Recall the formula for Simple Interest: SI = (P × R × T) / 100. Calculate the SI.
Recall the formula for Compound Interest: CI = P(1 + R/100)^T - P. Calculate the CI.
Subtract the calculated SI from the CI to find the difference.
For a quicker solution, recognize that the time period is 2 years and use the shortcut formula: Difference = P(R/100)². This avoids calculating SI and CI separately.
Substitute the values into the shortcut formula and solve to find the final answer.

Concept Tested & Keywords

Concept Tested: Difference between Simple Interest and Compound Interest
Stem keywords: simple interest, compound interest, difference, Rs. 1500, 5% per annum, 2 years
Lead-in keywords: difference between

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