Mathematics of FinanceMCQPYQ Dec 22Question 1460 of 512
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Raju invests ₹20,000\displaystyle ₹ 20,000 every year in a deposit scheme starting from today for next $12$ years. Assuming that interest rate on this deposit is $7\%$ 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₹540,526\displaystyle ₹ 540,526
  • B$382,813$
  • C$643,483$
  • D$357,769$

Detailed Solution & Explanation

Let the annual investment be A=Rs. 20,000\displaystyle A = Rs. \displaystyle \text{Rs. }20,000. Given parameters: * Time (n\displaystyle n) = $12$ years * Interest Rate (r\displaystyle r) = 7%\displaystyle 7\% p.a., so i=0.07\displaystyle i = 0.07 Since the investment starts today, this is an annuity due. The formula for the Future Value of an annuity due (FVdue\displaystyle FV_{due\displaystyle \text{due}}) is: FVdue=A×(1+i)n−1i×(1+i)FV_{due\displaystyle \text{due}} = A ×\displaystyle \times (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} ×\displaystyle \times (1+i) Substituting the values: FVdue=20,000×(1.07)12−10.07×1.07FV_{due\displaystyle \text{due}} = 20,000 ×\displaystyle \times (1.07)12−10.07\displaystyle \frac{(1.07)^{12} - 1}{0.07} ×\displaystyle \times 1.07 First, let's calculate (1.07)12\displaystyle (1.07)^{12}: (1.07)12≈2.252192(1.07)^{12} ≈\displaystyle \approx 2.252192 Now substitute this back: FVdue=20,000×2.252192−10.07×1.07FV_{due\displaystyle \text{due}} = 20,000 ×\displaystyle \times 2.252192−10.07\displaystyle \frac{2.252192 - 1}{0.07} ×\displaystyle \times 1.07 FVdue=20,000×1.2521920.07×1.07FV_{due\displaystyle \text{due}} = 20,000 ×\displaystyle \times 1.2521920.07\displaystyle \frac{1.252192}{0.07} ×\displaystyle \times 1.07 FVdue=20,000×17.88846×1.07=3,82,813FV_{due\displaystyle \text{due}} = 20,000 ×\displaystyle \times 17.88846 ×\displaystyle \times 1.07 = 3,82,813 Thus, the future value of the annuity is approximately Rs. 3,82,813\displaystyle Rs. \displaystyle \text{Rs. }3,82,813. 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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