A sum of money doubles itself in 8 years at simple interest. W... | Mathematics MCQ | Examoogle

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A sum of money doubles itself in 8 years at simple interest. What is the rate of interest?

$12.5\%$

$10\%$

$15\%$

$8\%$

Correct Answer

📐 MA • Math Direct FormulaMathematicsMathematics

Option A

$12.5\%$

Quick Summary:

Use the direct formula $R = \frac{(n-1) \times 100}{T}$ where $n$ is the multiple of the principal to save exam time.

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📐MAMath SolutionDirect Formula

📋 Given

Principal P, Amount becomes 2P, Time T = 8 years

🔢 Formula Used

R=(n−1)×100TR = \frac{(n - 1) \times 100}{T}R=T(n−1)×100​

⚡ Exam Hall Shortcut / Speed Trick

Use the direct formula $R = \frac{(n-1) \times 100}{T}$ where $n$ is the multiple of the principal to save exam time.

⚠️ Common Student Trap / Pitfall

Students often mistakenly take the simple interest as equal to the total amount ( $2P$ ) rather than the interest earned ( $2P - P = P$ ).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Given Values

Let the principal be $P$ . Since the sum doubles, the amount becomes $A = 2P$ in time $T = 8$ years.

A=2P,T=8 yearsA = 2P, \quad T = 8 \text{ years}A=2P,T=8 years

Calculate Simple Interest

The simple interest is the difference between the final amount and the principal: $SI = A - P = 2P - P = P$ .

SI=PSI = PSI=P

Apply Simple Interest Formula

Substitute the values into the formula $SI = \frac{P \times R \times T}{100}$ to solve for rate $R$ .

P=P×R×8100P = \frac{P \times R \times 8}{100}P=100P×R×8​

Solve for Rate of Interest

Dividing both sides by $P$ gives $1 = \frac{8R}{100}$ , leading to $R = \frac{100}{8} = 12.5\%$ .

R=1008=12.5%R = \frac{100}{8} = 12.5\%R=8100​=12.5%

✅

A is correct because the calculated rate of interest is 12.5%.

Core Concepts Used

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Simple Interest Principal and Amount Relationship Rate of Interest Calculation

💡 EXAM TIP

This direct multiple-time formula can also be adapted for compound interest problems using logarithms or successive multipliers.

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