Mathematics of FinanceMCQPYQ Dec 22Question 1458 of 512
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How much amount is required to be invested every year so as to accumulate 5,00,000\displaystyle ₹ 5,00,000 at the end of 12\displaystyle 12 years if interest is compounded annually at 10%\displaystyle 10\% p.a (1.12,0.1)=21.384281\displaystyle (1.12, 0.1) = 21.384281

Options

A23381.65\displaystyle ₹ 23381.65
B24385.85\displaystyle ₹ 24385.85
C26381.65\displaystyle ₹ 26381.65
D28362.75\displaystyle ₹ 28362.75
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Correct Answer

Option a23381.65\displaystyle ₹ 23381.65

All Options:

  • A23381.65\displaystyle ₹ 23381.65
  • B24385.85\displaystyle ₹ 24385.85
  • C26381.65\displaystyle ₹ 26381.65
  • D28362.75\displaystyle ₹ 28362.75

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Detailed Solution & Explanation

Let the annual investment be A\displaystyle A. Given parameters: * Target Future Value (FV\displaystyle FV) = Rs. 5,00,000\displaystyle \text{Rs. }5,00,000 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a., so i=0.10\displaystyle i = 0.10 * Given factor (1.10)12\displaystyle (1.10)^{12} cumulative growth factor (or FVIFA(12,0.10)\displaystyle FVIFA(12, 0.10)) = 21.384281\displaystyle 21.384281 The formula for the Future Value of an ordinary annuity is: FV=A×FVIFA(n,i)FV = A \times FVIFA(n, i) Substituting the values: 5,00,000=A×21.3842815,00,000 = A \times 21.384281 Solving for A\displaystyle A: A=5,00,00021.38428123,381.65A = \frac{5,00,000}{21.384281} \approx 23,381.65 Thus, the annual investment is approximately Rs. 23,381.65\displaystyle \text{Rs. }23,381.65. 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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