Mathematics of FinanceMCQPYQ 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 d10,000\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

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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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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