Mathematics for FinancePYQ Dec 22Question 1241 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 p.a.?

Options

A9%\displaystyle 9\%
B8%\displaystyle 8\%
C10%\displaystyle 10\%
D11%\displaystyle 11\%
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Correct Answer

✅ Option b — 8%\displaystyle 8\%

All Options:

  • A9%\displaystyle 9\%
  • B8%\displaystyle 8\%
  • C10%\displaystyle 10\%
  • D11%\displaystyle 11\%

Detailed Solution & Explanation

**Derivation of Interest Rate from Interest Difference** 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 (CI\displaystyle CI) and Simple Interest (SI\displaystyle 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.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

More Questions from Mathematics for Finance

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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