Mathematics of FinanceMCQPYQ June 19Question 1191 of 512
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A sum was invested for 3\displaystyle 3 years as per C.I. and the rate of interest for first year is 9%\displaystyle 9\%, 2nd\displaystyle 2^{nd} year is 6%\displaystyle 6\% and 3rd\displaystyle 3^{rd} year is 3%\displaystyle 3\% p.a. respectively. Find the sum if the amount in three years is Rs. 550\displaystyle \text{Rs. }550?

Options

ARs. 250\displaystyle \text{Rs. }250
BRs. 300\displaystyle \text{Rs. }300
CRs. 462.16\displaystyle \text{Rs. }462.16
DRs. 350\displaystyle \text{Rs. }350
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Correct Answer

Option cRs. 462.16\displaystyle \text{Rs. }462.16

All Options:

  • ARs. 250\displaystyle \text{Rs. }250
  • BRs. 300\displaystyle \text{Rs. }300
  • CRs. 462.16\displaystyle \text{Rs. }462.16
  • DRs. 350\displaystyle \text{Rs. }350

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Detailed Solution & Explanation

**Derivation of Sum (Principal) for Successive Compound Interest Rates** Given: - Future Value (A\displaystyle A) = Rs. 550\displaystyle \text{Rs. }550 - Time (t\displaystyle t) = 3\displaystyle 3 years - Successive Rates: r1=9%\displaystyle r_1 = 9\% (1st year), r2=6%\displaystyle r_2 = 6\% (2nd year), r3=3%\displaystyle r_3 = 3\% (3rd year) **Step 1: Set up the successive compound interest equation** A=P(1+r1)(1+r2)(1+r3)A = P(1 + r_1)(1 + r_2)(1 + r_3) 550=P(1+9100)(1+6100)(1+3100)550 = P\left(1 + \frac{9}{100}\right)\left(1 + \frac{6}{100}\right)\left(1 + \frac{3}{100}\right) **Step 2: Substitute and simplify the expression** 550=P×1.09×1.06×1.03550 = P \times 1.09 \times 1.06 \times 1.03 550=P×1.190062550 = P \times 1.190062 **Step 3: Solve for P\displaystyle P** P=5501.190062Rs. 462.16P = \frac{550}{1.190062} \approx \text{Rs. }462.16 Hence, **Option C** 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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