Mathematics for FinanceMTP Jun 23 Series IQuestion 1380 of 512
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The difference between compound interest and simple interest on an amount of 15,000\displaystyle 15,000 for 2\displaystyle 2 years is 96\displaystyle 96. What is the rate of interest per annum?

Options

A9%\displaystyle 9\%
B8%\displaystyle 8\%
C11%\displaystyle 11\%
D10%\displaystyle 10\%
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Correct Answer

✅ Option b — 8%\displaystyle 8\%

All Options:

  • A9%\displaystyle 9\%
  • B8%\displaystyle 8\%
  • C11%\displaystyle 11\%
  • D10%\displaystyle 10\%

Detailed Solution & Explanation

**Derivation of Interest Rate** Given: - Principal (P\displaystyle P) = Rs. 15,000\displaystyle \text{Rs. }15,000 - Time (t\displaystyle t) = 2\displaystyle 2 years - Difference between Compound Interest and Simple Interest (CI−SI\displaystyle CI - SI) = Rs. 96\displaystyle \text{Rs. }96 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2\text{Difference} = P \left(\frac{r}{100}\right)^2 96=15000(r100)296 = 15000 \left(\frac{r}{100}\right)^2 96=15000×r21000096 = 15000 \times \frac{r^2}{10000} 96=1.5r296 = 1.5 r^2 **Step 2: Solve for r\displaystyle r** r2=961.5=64r^2 = \frac{96}{1.5} = 64 r=64=8% per annumr = \sqrt{64} = 8\% \text{ per annum} Hence, **Option B** is the correct answer.

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