Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 1529 of 512
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How much amount is required to be invested every year as to accumulate 6,00,000\displaystyle 6,00,000 at the end of 10th\displaystyle 10^{th} year, if interest is compounded annually at 10%\displaystyle 10\% rate of interest?

Options

A37,467\displaystyle 37,467
B37,476\displaystyle 37,476
C37,647\displaystyle 37,647
D37,674\displaystyle 37,674
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Correct Answer

Option b37,476\displaystyle 37,476

All Options:

  • A37,467\displaystyle 37,467
  • B37,476\displaystyle 37,476
  • C37,647\displaystyle 37,647
  • D37,674\displaystyle 37,674

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Detailed Solution & Explanation

The annual contribution (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) = 6,00,000\displaystyle 6,00,000 * 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: Annuity factor=(1.10)1010.102.59374210.10=15.93742\text{Annuity factor} = \frac{(1.10)^{10} - 1}{0.10} \approx \frac{2.593742 - 1}{0.10} = 15.93742 A=6,00,00015.9374237,647.27A = \frac{6,00,000}{15.93742} \approx 37,647.27 Mathematically, the annual contribution is 37,647\displaystyle 37,647 (Option C). However, the official key marks Option B (37,476\displaystyle 37,476). 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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