Mathematics for FinancePYQ Jun 23Question 1245 of 512
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The difference between compound interest and simple interest on a certain sum of money invested for 3\displaystyle 3 years at 6%\displaystyle 6\% per annum is 110.16\displaystyle 110.16. The principal is

Options

A3,000\displaystyle 3,000
B3,700\displaystyle 3,700
C12,000\displaystyle 12,000
D10,000\displaystyle 10,000
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Correct Answer

✅ Option d — 10,000\displaystyle 10,000

All Options:

  • A3,000\displaystyle 3,000
  • B3,700\displaystyle 3,700
  • C12,000\displaystyle 12,000
  • D10,000\displaystyle 10,000

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Time (t\displaystyle t) = 3\displaystyle 3 years - Rate of Interest (r\displaystyle r) = 6%\displaystyle 6\% per annum - Difference between Compound Interest (CI\displaystyle CI) and Simple Interest (SI\displaystyle SI) = Rs. 110.16\displaystyle \text{Rs. }110.16 **Step 1: Use the difference formula for 3 years** Difference=P[3(r100)2+(r100)3]\text{Difference} = P \left[ 3 \left(\frac{r}{100}\right)^2 + \left(\frac{r}{100}\right)^3 \right] 110.16=P[3(0.06)2+(0.06)3]110.16 = P \left[ 3(0.06)^2 + (0.06)^3 \right] 110.16=P[3(0.0036)+0.000216]110.16 = P \left[ 3(0.0036) + 0.000216 \right] 110.16=P[0.0108+0.000216]110.16 = P [ 0.0108 + 0.000216 ] 110.16=0.011016P110.16 = 0.011016 P **Step 2: Solve for Principal (P\displaystyle P)** P=110.160.011016=Rs. 10,000P = \frac{110.16}{0.011016} = \text{Rs. }10,000 Hence, **Option D** is the correct answer.

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