Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1519 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 12%(0.12)\displaystyle 12\% (0.12). [1.384288]\displaystyle [1.384288]

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

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) = 12\displaystyle 12 years * Interest rate (i\displaystyle i) = 12%\displaystyle 12\% p.a. = 0.12\displaystyle 0.12 Substituting the values: Annuity factor=(1.12)1210.123.89597610.12=24.13313\text{Annuity factor} = \frac{(1.12)^{12} - 1}{0.12} \approx \frac{3.895976 - 1}{0.12} = 24.13313 A=5,00,00024.1331320,718.36A = \frac{5,00,000}{24.13313} \approx 20,718.36 Mathematically, the annual contribution is 20,718.36\displaystyle 20,718.36. However, the official key marks Option A (23381.65\displaystyle 23381.65). 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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