If a certain sum of money becomes double in 12 years simple interest, what will be the rate of interest per annum?

Appeared in: HPSSC - 2015

Explanation

The problem states that a sum of money doubles in 12 years. This means the Simple Interest (SI) earned is equal to the original Principal (P).
The formula for Simple Interest is SI = (P × R × T) / 100.
Substituting the values: P = (P × R × 12) / 100.
Solving for R gives: R = 100 / 12, which equals 8.33...%.
This value is correctly represented as 8.3% among the options.

Option B: If the rate were 10%, the time taken for the money to double (i.e., for SI to equal P) would be T = (SI × 100) / (P × R) = (P × 100) / (P × 10) = 10 years, not 12 years.
Option C: If the rate were 12%, the time taken for the money to double would be T = (P × 100) / (P × 12) = 100 / 12 = 8.33 years, not 12 years. This incorrectly swaps the rate and time values from the question.
Option D: The calculation yields a definite answer of 8.33...%, which is available as option A. Therefore, 'None' is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the rate of interest in a simple interest problem as background academic context rather than a clinical decision trigger.
While this is a mathematics question, the underlying skill of performing accurate calculations is critical in nursing.
Nurses frequently use formulas for tasks such as calculating drug dosages, IV drip rates, and patient intake/output, where precision is essential for patient safety.
What if? If the question involved compound interest instead of simple interest, the formula would be A = P(1 + R/n)^(nt), and the calculation for the rate would be more complex, yielding a different, lower rate.

How to Approach the Question

First, identify the type of problem: this is a simple interest calculation.
Let the principal be 'P'. Read the question carefully to determine the final amount. Here, it 'becomes double', so the Amount is 2P.
Calculate the Simple Interest (SI) earned: SI = Amount - Principal = 2P - P = P.
Recall the formula for Simple Interest: SI = (P × R × T) / 100.
Substitute the known values (SI = P, T = 12) into the formula.
Solve the resulting algebraic equation for the unknown variable, which is the Rate (R).

Concept Tested & Keywords

Concept Tested: Calculation of the rate of interest in a simple interest problem.
Stem keywords: sum of money, double, 12 years, simple interest, rate of interest
Lead-in keywords: what will be

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Practise the full HPSSC - 2015

Attempt every question from this paper in a timed mock, then review the full solution for each one.