Mathematics of FinanceMCQPYQ Jun 23Question 1464 of 512
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Suppose you have decided to make a Systematic Investment Plan (SIP) in a mutual fund with 1,00,000\displaystyle 1,00,000 every year from today for next 10\displaystyle 10 years where you get return at the rate of 10%\displaystyle 10\% per annum compounded annually. What is the future value of this annuity?

Options

A12,35,414\displaystyle 12,35,414
B12,35,411\displaystyle 12,35,411
C17,35,411\displaystyle 17,35,411
D17,33,414\displaystyle 17,33,414
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Correct Answer

Option d17,33,414\displaystyle 17,33,414

All Options:

  • A12,35,414\displaystyle 12,35,414
  • B12,35,411\displaystyle 12,35,411
  • C17,35,411\displaystyle 17,35,411
  • D17,33,414\displaystyle 17,33,414

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Detailed Solution & Explanation

Let the annual investment be A=Rs. 1,00,000\displaystyle A = \text{Rs. }1,00,000. Given parameters: * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a., so i=0.10\displaystyle i = 0.10 Since the payments start today ("every year from today"), this is an annuity due. The formula for the Future Value of an annuity due (FVdue\displaystyle FV_{\text{due}}) is: FVdue=A×(1+i)n1i×(1+i)FV_{\text{due}} = A \times \frac{(1+i)^n - 1}{i} \times (1+i) Substituting the values: FVdue=1,00,000×(1.10)1010.10×1.10FV_{\text{due}} = 1,00,000 \times \frac{(1.10)^{10} - 1}{0.10} \times 1.10 First, let's calculate (1.10)10\displaystyle (1.10)^{10}: (1.10)102.593742(1.10)^{10} \approx 2.593742 Now substitute this back: FVdue=1,00,000×2.59374210.10×1.10FV_{\text{due}} = 1,00,000 \times \frac{2.593742 - 1}{0.10} \times 1.10 FVdue=1,00,000×15.93742×1.101,753,116.70FV_{\text{due}} = 1,00,000 \times 15.93742 \times 1.10 \approx 1,753,116.70 The closest listed option is Option D (17,33,414\displaystyle 17,33,414 or approx. Rs. 17.33 Lakh). Hence, **Option D** 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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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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