Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1520 of 512
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Raju invests 20,000\displaystyle 20,000 every year in a deposit scheme starting from today for next 12\displaystyle 12 years. Assuming that interest rate on his deposit is 7%\displaystyle 7\% per annum compounded annually. What will be the future value of this annuity?

Options

A540,576\displaystyle 540,576
B382,813\displaystyle 382,813
C643,483\displaystyle 643,483
D357,769\displaystyle 357,769
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Correct Answer

Option b382,813\displaystyle 382,813

All Options:

  • A540,576\displaystyle 540,576
  • B382,813\displaystyle 382,813
  • C643,483\displaystyle 643,483
  • D357,769\displaystyle 357,769

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Detailed Solution & Explanation

Since payments are made starting today, this is an annuity due. The future value (FVdue\displaystyle FV_{\text{due}}) is: FVdue=A[(1+i)n1i]×(1+i)FV_{\text{due}} = A \left[ \frac{(1+i)^n - 1}{i} \right] \times (1+i) Given: * Annual investment (A\displaystyle A) = 20,000\displaystyle 20,000 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest rate (i\displaystyle i) = 7%\displaystyle 7\% p.a. = 0.07\displaystyle 0.07 Substituting the values: Annuity factor=(1.07)1210.072.2521910.07=17.88845\text{Annuity factor} = \frac{(1.07)^{12} - 1}{0.07} \approx \frac{2.25219 - 1}{0.07} = 17.88845 FVdue=20,000×17.88845×1.073,82,812.83FV_{\text{due}} = 20,000 \times 17.88845 \times 1.07 \approx 3,82,812.83 This matches Option B (382,813\displaystyle 382,813). Hence, **Option B** 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.

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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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