At what rate of Simple Interest will a sum of money double itself in 10 years?

Appeared in: DSSSB 6 September 2024

Explanation

For a sum of money to double, the total Simple Interest (SI) earned over the period must be equal to the original Principal (P) amount.
The formula for Simple Interest is SI = (P × R × T) / 100.
Given that SI = P and Time (T) = 10 years, the formula becomes P = (P × R × 10) / 100.
Solving for R, we can cancel P from both sides, giving 1 = (R × 10) / 100.
This simplifies to 1 = R / 10, which means R = 10.
Therefore, the required rate of interest is 10%.

Option A: At a 5% rate, the interest earned in 10 years would be (P × 5 × 10) / 100 = 0.5P. The total amount would be P + 0.5P = 1.5P, which is not double the principal.
Option B: At an 8% rate, the interest earned in 10 years would be (P × 8 × 10) / 100 = 0.8P. The total amount would be P + 0.8P = 1.8P, which is less than double.
Option D: At a 12% rate, the interest earned in 10 years would be (P × 12 × 10) / 100 = 1.2P. The total amount would be P + 1.2P = 2.2P, which is more than double.

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 when the principal amount doubles over a given period as background academic context rather than a clinical decision trigger.
Understanding simple interest is a fundamental skill for personal financial literacy, crucial for managing loans, savings, and investments.
This concept is foundational for more complex financial calculations, including compound interest, annuities, and loan amortizations, which are relevant for long-term financial planning.
What if the interest was compounded annually? If the interest were compounded, the rate needed to double the money in 10 years would be lower than 10%. The formula would be A = P(1 + R/100)^T. Solving 2P = P(1 + R/100)^10 gives R ≈ 7.18%. This shows that compounding allows money to grow faster.

How to Approach the Question

First, identify the key information given: the time period is 10 years.
Translate the phrase 'double itself' into a mathematical relationship: Final Amount (A) = 2 × Principal (P).
From this, deduce the total Simple Interest (SI) required: SI = A - P = 2P - P = P.
Recall the standard formula for Simple Interest: SI = (P × R × T) / 100.
Substitute the known values (SI = P and T = 10) into the formula.
Solve the resulting algebraic equation for the unknown variable, R (Rate).

Concept Tested & Keywords

Concept Tested: Calculating the rate of simple interest when the principal amount doubles over a given period.
Stem keywords: Simple Interest, sum of money, double, 10 years
Lead-in keywords: At what rate
Negative lead-in flag: false

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Practise the full DSSSB 6 September 2024

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