The compound interest on a sum of ₹10000 for 2 years is ₹2544,... | Mathematics MCQ | Examoogle

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MathematicsSimple & Compound Interest

The compound interest on a sum of ₹10000 for 2 years is ₹2544, when the interest is compounded annually. If the rate of interest per annum is halved and the time duration is doubled, then the compound interest (in ₹, correct to nearest paise) will be:

2724.67

2642.77

2742.67

2624.77

Correct Answer

📐 MA • Math Formula SubstitutionMathematicsSimple & Compound Interest

Option D

2624.77

Quick Summary:

Use the growth factor approach: for 2 years, $CI = P \times [(1+r)^2 - 1]$ . Since $2544/10000 = 0.2544$ , it is clear that $(1+r)^2 = 1.2544$ , meaning $1+r = 1.12$ , so $r = 12\%$ .

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📐MAMath SolutionFormula Substitution

📋 Given

Principal P = 10000, Compound Interest CI = 2544, Time T = 2 years

🔢 Formula Used

A=P(1+R100)nA = P \left(1 + \frac{R}{100}\right)^nA=P(1+100R​)n

⚡ Exam Hall Shortcut / Speed Trick

Use the growth factor approach: for 2 years, $CI = P \times [(1+r)^2 - 1]$ . Since $2544/10000 = 0.2544$ , it is clear that $(1+r)^2 = 1.2544$ , meaning $1+r = 1.12$ , so $r = 12\%$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the interest for the new rate by simply halving the interest amount; however, compound interest is non-linear and must be recalculated with the new parameters.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Find the initial rate R

Given $A = P + CI = 10000 + 2544 = 12544$ . Using the amount formula $12544 = 10000(1 + R/100)^2$ , we get $(1 + R/100)^2 = 1.2544$ . Taking the square root, $1 + R/100 = 1.12$ , so $R = 12\%$ .

R=12%R = 12\%R=12%

Adjust rate and time

New rate $R' = R/2 = 12\%/2 = 6\%$ . New time $n' = 2 \times 2 = 4$ years.

R′=6%,n′=4R' = 6\%, \quad n' = 4R′=6%,n′=4

Calculate new Compound Interest

Calculate $A' = P(1 + R'/100)^{n'} = 10000(1 + 6/100)^4 = 10000(1.06)^4$ . Calculating $(1.06)^4 = 1.26247696$ . Thus $A' = 12624.7696$ .

A′=10000×1.26247696=12624.77A' = 10000 \times 1.26247696 = 12624.77A′=10000×1.26247696=12624.77

Final Interest Calculation

Subtract the principal from the new amount: $CI' = A' - P = 12624.7696 - 10000 = 2624.7696$ . Rounding to the nearest paise gives $2624.77$ .

CI′=2624.77CI' = 2624.77CI′=2624.77

✅

D is correct because the recalculated interest with a rate of 6% over 4 years yields a total of 2624.77.

Core Concepts Used

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Compound Interest Rate Adaptation Exponential Growth

💡 EXAM TIP

This logic is identical to population growth models where $P(t) = P_0(1+r)^t$ ; always verify if the compounding frequency changes (e.g., half-yearly) which would alter the formula to $R/2$ and $2T$ .

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