Solve this multiple-choice question and choose the correct option.

Problem restatementFor 2 years at rate r, CI − SI = P r2. Use this identity to solve for r. Given data P = 15,000; CI − SI = 96 Concept/ApproachFor two years, CI = P(2r + r2) and SI = P(2r); their difference is P r2. Step-by-step calculationP r2 = 96 ⇒ 15,000 r2 = 96r2 = 96 ÷ 15,000 = 0.0064r = √0.0064 = 0.08 = 8% p.a. Common pitfallsUsing 96 as one year difference (the identity holds specifically for 2 years). Final Answer8% p.a.

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The difference between compound and simple interest on Rs. 15,000 for 2 years is Rs. 96. What is the annual rate of interest?

Difficulty: Easy

6% p.a.
7% p.a.
8% p.a.
9% p.a.
None of these

Correct Answer: 8% p.a.

Explanation:

Problem restatementFor 2 years at rate r, CI − SI = P r². Use this identity to solve for r.

Given data

P = 15,000; CI − SI = 96

Concept/ApproachFor two years, CI = P(2r + r²) and SI = P(2r); their difference is P r².

Step-by-step calculationP r² = 96 ⇒ 15,000 r² = 96r² = 96 ÷ 15,000 = 0.0064r = √0.0064 = 0.08 = 8% p.a.

Common pitfallsUsing 96 as one year difference (the identity holds specifically for 2 years).

Final Answer8% p.a.

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