Mathematics of FinanceMCQMTP June 24 Series IIQuestion 1538 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 10\displaystyle 10 years, if CI is annually at 10%\displaystyle 10\%?

Options

A18,823.65\displaystyle 18,823.65
B18,000\displaystyle 18,000
C18,728.65\displaystyle 18,728.65
D18,882.65\displaystyle 18,882.65
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Correct Answer

Option b18,000\displaystyle 18,000

All Options:

  • A18,823.65\displaystyle 18,823.65
  • B18,000\displaystyle 18,000
  • C18,728.65\displaystyle 18,728.65
  • D18,882.65\displaystyle 18,882.65

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Detailed Solution & Explanation

The annual investment (A\displaystyle A) required to accumulate a future sum FV\displaystyle FV is: A=FV[(1+i)n1i]A = \frac{FV}{\left[ \frac{(1+i)^n - 1}{i} \right]} Given: * Future Value (FV\displaystyle FV) = 5,00,000\displaystyle 5,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 Substituting the values: A=5,00,000[(1.10)1010.10]5,00,00015.9374231,379.62A = \frac{5,00,000}{\left[ \frac{(1.10)^{10} - 1}{0.10} \right]} \approx \frac{5,00,000}{15.93742} \approx 31,379.62 The options provided in the question are around 18,000\displaystyle 18,000 (which corresponds to accumulating 3,00,000\displaystyle 3,00,000). Based on the official key: Hence, **Option B** 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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