A sum of Rs. 12,500 amount to Rs.15,500 in 4 years at the rate of simple interest. What is the rate of interest?

Appeared in: NCL (MP) Nursing Officer - 2019

Explanation

The first step is to determine the total interest earned over the 4-year period. This is the difference between the final amount (Rs. 15,500) and the initial principal (Rs. 12,500), which is Rs. 3,000.
The formula for Simple Interest (SI) is SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.
To find the rate (R), the formula is rearranged to R = (SI × 100) / (P × T).
Plugging in the values: R = (3000 × 100) / (12500 × 4).
Solving the equation gives R = 300000 / 50000, which simplifies to R = 6.
Therefore, the annual rate of interest is 6%.

Option A: If the rate were 3%, the simple interest for 4 years would be (12500 × 3 × 4) / 100 = Rs. 1,500. The final amount would be 12,500 + 1,500 = Rs. 14,000, which does not match the given amount of Rs. 15,500.
Option B: If the rate were 4%, the simple interest for 4 years would be (12500 × 4 × 4) / 100 = Rs. 2,000. The final amount would be 12,500 + 2,000 = Rs. 14,500, not Rs. 15,500.
Option C: If the rate were 5%, the simple interest for 4 years would be (12500 × 5 × 4) / 100 = Rs. 2,500. The final amount would be 12,500 + 2,500 = Rs. 15,000, which is less than the given amount of Rs. 15,500.

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 skill required for various competitive exams, including those for nursing positions.
While not a direct clinical skill, mathematical proficiency is crucial for nurses in tasks like medication dosage calculation, interpreting lab results, and managing fluid balances.
Financial literacy is a valuable life skill for nurses to manage personal finances and understand healthcare economics on a broader scale.

How to Approach the Question

First, identify all the given values in the problem: Principal (P), Final Amount (A), and Time (T).
Calculate the total Simple Interest (SI) earned by subtracting the Principal from the Final Amount (SI = A - P).
Recall the standard formula for Simple Interest: SI = (P × R × T) / 100.
Rearrange this formula to isolate the variable you need to find, which is the Rate (R). The rearranged formula is R = (SI × 100) / (P × T).
Substitute the known values (SI, P, T) into the rearranged formula.
Perform the calculation to find the value of R, which will be the interest rate in percent.

Concept Tested & Keywords

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