Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1520 of 512
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Raju invests $20,000$ every year in a deposit scheme starting from today for next $12$ 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?

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

✅ Option b — $382,813$

All Options:

  • A$540,576$
  • B$382,813$
  • C$643,483$
  • D$357,769$

Detailed Solution & Explanation

Since payments are made starting today, this is an annuity due. The future value (FVdue\displaystyle FV_{due\displaystyle \text{due}}) is: FVdue=A[(1+i)n−1i]×(1+i)FV_{due\displaystyle \text{due}} = A \left[ (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} \right] ×\displaystyle \times (1+i) Given: * Annual investment (A\displaystyle A) = $20,000$ * Time (n\displaystyle n) = $12$ years * Interest rate (i\displaystyle i) = 7%\displaystyle 7\% p.a. = $0.07$ Substituting the values: Annuity factor=(1.07)12−10.07≈2.25219−10.07=17.88845\displaystyle \text{Annuity factor} = \frac{(1.07)^{12} - 1}{0.07} ≈\displaystyle \approx 2.25219−10.07=17\displaystyle \frac{2.25219 - 1}{0.07} = 17.88845 FVdue=20,000×17.88845×1.07≈3,82,812.83FV_{due\displaystyle \text{due}} = 20,000 ×\displaystyle \times 17.88845 ×\displaystyle \times 1.07 ≈\displaystyle \approx 3,82,812.83 This matches Option B ($382,813$). 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.

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.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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