After 4 years the principal amount of Rs. 12000 grows into Rs. 14,400. Find out the rate of simple interest?

Appeared in: OSSSC Nursing Officer-2021

Explanation

The first step is to calculate the total simple interest (SI) earned over the 4-year period. This is the difference between the final amount (A) and the initial principal (P).
SI = Amount - Principal = Rs. 14,400 - Rs. 12,000 = Rs. 2,400.
The formula for simple interest is SI = (P × R × T) / 100. To find the rate (R), we rearrange this to R = (SI × 100) / (P × T).
Substituting the values: R = (2400 × 100) / (12000 × 4).
This simplifies to R = 240000 / 48000, which equals 5.
Therefore, the annual rate of simple interest is 5%.

Option A: A rate of 3% would result in a total interest of (12000 × 3 × 4) / 100 = Rs. 1,440, leading to a final amount of Rs. 13,440, which is incorrect.
Option C: A rate of 4% would result in a total interest of (12000 × 4 × 4) / 100 = Rs. 1,920, leading to a final amount of Rs. 13,920, which is incorrect.
Option D: A rate of 6% would result in a total interest of (12000 × 6 × 4) / 100 = Rs. 2,880, leading to a final amount of Rs. 14,880, which is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Simple Interest Rate as background academic context rather than a clinical decision trigger.
This question tests general quantitative aptitude, a non-nursing subject area often included in competitive examinations for recruitment.
Strong numerical skills are essential for various nursing tasks, including medication dosage calculations, interpreting lab results, and managing fluid balances, even though this specific problem is financial.
What if the interest was compounded annually? The calculation would be more complex, using the formula A = P(1 + R/100)^T. The rate would be different and lower than the simple interest rate for the same final amount.

How to Approach the Question

First, carefully read the question to identify the given values: Principal (P = 12000), final Amount (A = 14400), and Time (T = 4 years).
Recognize that the question asks for the 'rate of simple interest', indicating the use of the simple interest formula.
Calculate the total Simple Interest (SI) earned by subtracting the principal from the final amount: SI = A - P.
Recall the formula for simple interest: SI = (P × R × T) / 100.
Rearrange this formula to solve for the unknown variable, which is the Rate (R): R = (SI × 100) / (P × T).
Substitute the known values into the rearranged formula and perform the calculation to find the rate.

Concept Tested & Keywords

Concept Tested: Calculation of Simple Interest Rate
Stem keywords: principal amount, grows into, rate of simple interest, Rs. 12000, Rs. 14,400, 4 years
Lead-in keywords: Find out

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