Mathematics of FinanceMCQPYQ Dec 22Question 1236 of 512
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If $64$ amount to $83.20$ in 2\displaystyle 2 years, what will $86$ amount to in $4$ years at the same Rate percent per annum?

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

✅ Option c — $145.34$

All Options:

  • A$127.60$
  • B$147.60$
  • C$145.34$
  • D$117.60$

Detailed Solution & Explanation

**Derivation of Future Amount under Compound Interest** Given: - Principal 1 (P1\displaystyle P_1) = Rs. 64\displaystyle Rs. \displaystyle \text{Rs. }64 - Amount 1 (A1\displaystyle A_1) = Rs. 83.20\displaystyle Rs. \displaystyle \text{Rs. }83.20 - Time 1 (t1\displaystyle t_1) = 2\displaystyle 2 years **Step 1: Determine the rate of interest using compounding** A1=P1(1+r)t1A_1 = P_1(1 + r)^{t_1} 83.20=64(1+r)283.20 = 64(1 + r)^2 83.2064=(1+r)283.2064\displaystyle \frac{83.20}{64} = (1 + r)^2 1.30=(1+r)21.30 = (1 + r)^2 **Step 2: Calculate the future amount (A2\displaystyle A_2) of Rs. 86 in 4\displaystyle 4 years (t2=4\displaystyle t_2 = 4)** A2=P2(1+r)t2A_2 = P_2(1 + r)^{t_2} A2=86(1+r)4A_2 = 86(1 + r)^4 A2=86[(1+r)2]2A_2 = 86 \left[(1 + r)^2\right]^2 Using the value (1+r)2=1.30\displaystyle (1+r)^2 = 1.30: A2=86(1.30)2A_2 = 86(1.30)^2 A2=86×1.69=Rs. 145.34A_2 = 86 ×\displaystyle \times 1.69 = Rs. \displaystyle \text{Rs. }145.34 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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