After 4 years, a principal amount of Rs. 12000 grows into Rs. 14400. Find out the rate of simple interest.

Appeared in: NORCET 2 - 2021 (shift-1)

Explanation

First, calculate the total Simple Interest (SI) earned by subtracting the Principal (P) from the final Amount (A). Here, SI = Rs. 14400 - Rs. 12000 = Rs. 2400.
Next, use the formula for Simple Interest, which is SI = (P × R × T) / 100, where R is the rate and T is the time.
Rearrange the formula to solve for the Rate (R): R = (SI × 100) / (P × T).
Substitute the values: R = (2400 × 100) / (12000 × 4).
Solving the equation gives R = 240000 / 48000, which simplifies to R = 5. Therefore, the rate is 5%.

Option A: If the rate were 6%, the simple interest would be (12000 × 6 × 4) / 100 = Rs. 2880. This does not match the calculated interest of Rs. 2400.
Option C: If the rate were 4%, the simple interest would be (12000 × 4 × 4) / 100 = Rs. 1920. This is less than the actual interest of Rs. 2400.
Option D: If the rate were 3%, the simple interest would be (12000 × 3 × 4) / 100 = Rs. 1440. This is significantly lower than the actual interest of Rs. 2400.

Visual 1: Infographic - A clear visual breakdown of the simple interest formulas: SI = A - P and R = (SI × 100) / (P × T), with each variable clearly labeled.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the rate of simple interest given the principal, amount, and time as background academic context rather than a clinical decision trigger.
This question tests basic quantitative aptitude, a skill essential for various competitive examinations, including those for nursing positions.
While not a direct clinical calculation, the logical reasoning and mathematical accuracy required are transferable skills for tasks like medication dosage calculation and data interpretation.
What if the interest was compounded annually? The calculation would be more complex, using the formula A = P(1 + R/100)^T, and the resulting rate would be different.

How to Approach the Question

First, carefully read the question to identify all the given values: Principal (P), Amount (A), and Time (T).
Recognize that the interest earned is the difference between the final amount and the principal. Calculate this value first (Simple Interest, SI).
Recall the standard formula for Simple Interest: SI = (P × R × T) / 100.
Rearrange this formula algebraically to isolate the variable you need to find, which is the Rate (R).
Substitute the known values of P, SI, and T into the rearranged formula.
Perform the calculation carefully to find the value of R, which will be the interest rate in percent.

Concept Tested & Keywords

Concept Tested: Calculating the rate of simple interest given the principal, amount, and time.
Stem keywords: principal amount, Rs. 12000, grows into, Rs. 14400, 4 years, simple interest
Lead-in keywords: Find out

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