Mathematics of FinanceMCQPYQ Nov 18Question 1183 of 512
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A certain sum of money Q\displaystyle Q was deposited for 5\displaystyle 5 years and 4\displaystyle 4 months at 4.5%\displaystyle 4.5\% simple interest and amounted to Rs. 248\displaystyle \text{Rs. }248, then the value of Q\displaystyle Q is

Options

ARs. 200\displaystyle \text{Rs. }200
BRs. 210\displaystyle \text{Rs. }210
CRs. 220\displaystyle \text{Rs. }220
DRs. 240\displaystyle \text{Rs. }240
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Correct Answer

Option aRs. 200\displaystyle \text{Rs. }200

All Options:

  • ARs. 200\displaystyle \text{Rs. }200
  • BRs. 210\displaystyle \text{Rs. }210
  • CRs. 220\displaystyle \text{Rs. }220
  • DRs. 240\displaystyle \text{Rs. }240

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Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Amount (A\displaystyle A) = Rs. 248\displaystyle \text{Rs. }248 - Time (t\displaystyle t) = 5\displaystyle 5 years and 4\displaystyle 4 months = 5+412=5+13=163\displaystyle 5 + \frac{4}{12} = 5 + \frac{1}{3} = \frac{16}{3} years - Simple Interest Rate (r\displaystyle r) = 4.5%\displaystyle 4.5\% per annum **Step 1: Set up the Simple Interest Amount equation** A=Q(1+r×t100)A = Q\left(1 + \frac{r \times t}{100}\right) 248=Q(1+4.5×163100)248 = Q\left(1 + \frac{4.5 \times \frac{16}{3}}{100}\right) **Step 2: Simplify the term inside the parenthesis** Interest component=4.5×163×100=1.5×16100=24100=0.24\text{Interest component} = \frac{4.5 \times 16}{3 \times 100} = \frac{1.5 \times 16}{100} = \frac{24}{100} = 0.24 248=Q(1+0.24)248 = Q(1 + 0.24) 248=1.24Q248 = 1.24 Q **Step 3: Solve for Q\displaystyle Q** Q=2481.24=Rs. 200Q = \frac{248}{1.24} = \text{Rs. }200 Hence, **Option A** 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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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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