Mathematics of FinanceMCQPYQ Dec. 21Question 1451 of 512
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Mr. X wants to accumulate 50,00,000\displaystyle ₹ 50,00,000 at the end of 10\displaystyle 10 years. Then how much amount is required to be invested every year if interest is compounded annually at 10%\displaystyle 10\%? (Given that P(10,0.10)=15.9374298)\displaystyle P(10,0.10) = 15.9374298)

Options

A3,13,736.87\displaystyle ₹ 3,13,736.87
B4,13,726.87\displaystyle ₹ 4,13,726.87
C3,53,726.87\displaystyle ₹ 3,53,726.87
D4,53,726.87\displaystyle ₹ 4,53,726.87
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Correct Answer

Option a3,13,736.87\displaystyle ₹ 3,13,736.87

All Options:

  • A3,13,736.87\displaystyle ₹ 3,13,736.87
  • B4,13,726.87\displaystyle ₹ 4,13,726.87
  • C3,53,726.87\displaystyle ₹ 3,53,726.87
  • D4,53,726.87\displaystyle ₹ 4,53,726.87

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Detailed Solution & Explanation

Let the amount to be invested every year be A\displaystyle A. Given parameters: * Target Future Value (FV\displaystyle FV) = Rs. 50,00,000\displaystyle \text{Rs. }50,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a. compounded annually, so i=0.10\displaystyle i = 0.10 * Future Value Annuity Factor (FVIFA(10,0.10)\displaystyle FVIFA(10, 0.10)) 15.9374298\displaystyle \approx 15.9374298 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: 50,00,000=A×15.937429850,00,000 = A \times 15.9374298 Solving for A\displaystyle A: A=50,00,00015.93742983,13,726.87A = \frac{50,00,000}{15.9374298} \approx 3,13,726.87 Thus, the amount required to be invested is approximately Rs. 3,13,726.87\displaystyle \text{Rs. }3,13,726.87. 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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