Mathematics of FinanceMCQMTP May 19 Series IIQuestion 1501 of 512
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Suppose your friend decided gift to you 10000\displaystyle 10000 every year starting from today for the next five years. Your deposit this amount in a bank and when you receive and get 10%\displaystyle 10\% per annum interest compounded annually. What is the present value of this annuity?

Options

ARs. 42698.70\displaystyle 42698.70
BRs. 43698.70\displaystyle 43698.70
CRs. 45698.70\displaystyle 45698.70
DRs. 41698.70\displaystyle 41698.70
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Correct Answer

Option cRs. 45698.70\displaystyle 45698.70

All Options:

  • ARs. 42698.70\displaystyle 42698.70
  • BRs. 43698.70\displaystyle 43698.70
  • CRs. 45698.70\displaystyle 45698.70
  • DRs. 41698.70\displaystyle 41698.70

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Detailed Solution & Explanation

Since payments start today, this is an annuity due. The present value (PVdue\displaystyle PV_{\text{due}}) is: PVdue=A+A×P(4,0.10)PV_{\text{due}} = A + A \times P(4, 0.10) Given: * Annual payment (A\displaystyle A) = 10,000\displaystyle 10,000 * Factor P(4,0.10)=3.16987\displaystyle P(4, 0.10) = 3.16987 Substituting the values: PVdue=10,000+10,000×3.16987=41,698.70PV_{\text{due}} = 10,000 + 10,000 \times 3.16987 = 41,698.70 Mathematically, this is Option D. However, the official key marks Option C (45,698.70\displaystyle 45,698.70). 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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