Mathematics of FinanceMCQMTP June 24 Series IQuestion 1407 of 512
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How much money is required to be invested every year as to accumulate Rs.$6,00,000\displaystyle at the end of 10 years, if interest is compounded annually at $10\% rate of interest?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $37,647$

All Options:

  • A$37,467$
  • B$37,476$
  • C$37,647$
  • D$37,674$

Detailed Solution & Explanation

Let the amount to be invested every year be A\displaystyle A. This is a problem of finding the periodic payment of an ordinary annuity. Given parameters: * Future Value (FV\displaystyle FV) = Rs. 6,00,000\displaystyle Rs. \displaystyle \text{Rs. }6,00,000 * Rate of interest (r\displaystyle r) = $10\%p.a.,so\displaystyle p.a., soi = 0.10$ * Time (n\displaystyle n) = $10$ years The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A ×\displaystyle \times (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} Substituting the values: 6,00,000=A×(1.10)10−10.106,00,000 = A ×\displaystyle \times (1.10)10−10.10\displaystyle \frac{(1.10)^{10} - 1}{0.10} First, let's calculate (1.10)10\displaystyle (1.10)^{10}: (1.10)10≈2.59374246(1.10)^{10} ≈\displaystyle \approx 2.59374246 Now substitute this back: 6,00,000=A×2.59374246−10.106,00,000 = A ×\displaystyle \times 2.59374246−10.10\displaystyle \frac{2.59374246 - 1}{0.10} 6,00,000=A×1.593742460.106,00,000 = A ×\displaystyle \times 1.593742460.10\displaystyle \frac{1.59374246}{0.10} 6,00,000=15.9374246A6,00,000 = 15.9374246 A Solving for A\displaystyle A: A=6,00,00015.9374246≈37,647.23A = 6,00,00015.9374246\displaystyle \frac{6,00,000}{15.9374246} ≈\displaystyle \approx 37,647.23 Thus, the amount required to be invested every year is approximately Rs. 37,647\displaystyle Rs. \displaystyle \text{Rs. }37,647. Hence, **Option C** 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

Exam Strategy Tip

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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