If the simple interest on a certain sum of money for 3 years at 5% is Rs. 150, the corresponding CI is:

Appeared in: NHM MP Staff Nurse-2022

Explanation

The problem requires a two-step calculation: first finding the principal, then the compound interest.
The first step is to use the simple interest formula (SI = P×R×T/100) to find the principal amount.
Given SI=150, R=5%, and T=3 years, the principal (P) is calculated to be Rs. 1000.
The second step is to use this principal (Rs. 1000) to calculate the compound interest for the same rate and duration.
Using the formula CI = P[(1+R/100)^T - 1], the CI is 1000[(1.05)^3 - 1], which equals Rs. 157.625.
This calculated value matches the closest option, Rs. 157.62.

Option B: This value represents a calculation error. It is slightly higher than the correct amount and does not result from the correct application of the compound interest formula.
Option C: This value is illogical because it is significantly less than the simple interest (Rs. 150). For any period longer than one year, compound interest will always be greater than simple interest.
Option D: This value is incorrect. It is very close to the compound interest for 2 years (which is Rs. 102.50), suggesting an error where the time period was mistaken as 2 years instead of 3.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Compound Interest from Simple Interest as background academic context rather than a clinical decision trigger.
Understanding the difference between simple and compound interest is a fundamental financial literacy skill, crucial for personal and professional financial planning, including loans, savings, and investments.
For healthcare professionals, this can apply to understanding financing for a private practice, educational loans, or evaluating investment options for retirement.
What if? If the interest were compounded semi-annually, the number of periods would double (6) and the rate per period would be halved (2.5%). This would result in a slightly higher CI (Rs. 159.69), demonstrating the power of more frequent compounding.

How to Approach the Question

Identify the given values from the problem: Simple Interest (SI) = 150, Rate (R) = 5%, and Time (T) = 3 years.
Recognize that to find the Compound Interest (CI), you first need the Principal (P).
Use the Simple Interest formula, SI = (P × R × T) / 100, and rearrange it to solve for P: P = (SI × 100) / (R × T).
Calculate P: P = (150 × 100) / (5 × 3) = 1000.
Now, use the Principal (P=1000) in the Compound Interest formula: CI = P * [(1 + R/100)^T - 1].
Calculate CI: CI = 1000 * [(1.05)^3 - 1] = 1000 * [1.157625 - 1] = 157.625.

Concept Tested & Keywords

Concept Tested: Calculation of Compound Interest from Simple Interest
Stem keywords: simple interest, sum of money, 3 years, 5%, Rs. 150, compound interest
Lead-in keywords: the corresponding CI is

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