Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 1384 of 512
All Questions

A certain sum of money amounts to 5,000\displaystyle 5,000 in 5\displaystyle 5 years at 10%\displaystyle 10\% p.a. In how many years will it amount to 6,000\displaystyle 6,000 at same rate of S.I. p.a.

Options

A10\displaystyle 10 years
B8\displaystyle 8 years
C6\displaystyle 6 years
DNone of these
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Correct Answer

✅ Option b — 8\displaystyle 8 years

All Options:

  • A10\displaystyle 10 years
  • B8\displaystyle 8 years
  • C6\displaystyle 6 years
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Required Period** Given: - Amount in 5\displaystyle 5 years (A1\displaystyle A_1) = Rs. 5,000\displaystyle \text{Rs. }5,000 - Rate of simple interest (R\displaystyle R) = 10%\displaystyle 10\% per annum - Target Amount (A2\displaystyle A_2) = Rs. 6,000\displaystyle \text{Rs. }6,000 **Step 1: Calculate the Principal (P\displaystyle P) from the first scenario** A1=P(1+R×t1100)A_1 = P\left(1 + \frac{R \times t_1}{100}\right) 5000=P(1+10×5100)5000 = P\left(1 + \frac{10 \times 5}{100}\right) 5000=P(1+0.50)=1.50P5000 = P(1 + 0.50) = 1.50 P P=50001.50=Rs. 100003≈Rs. 3,333.33P = \frac{5000}{1.50} = \text{Rs. }\frac{10000}{3} \approx \text{Rs. }3,333.33 **Step 2: Find the time (t2\displaystyle t_2) to reach Rs. 6,000** A2=P(1+R×t2100)A_2 = P\left(1 + \frac{R \times t_2}{100}\right) 6000=100003(1+10×t2100)6000 = \frac{10000}{3}\left(1 + \frac{10 \times t_2}{100}\right) 1.80=1+0.10t21.80 = 1 + 0.10 t_2 0.10t2=0.80  ⟹  t2=8 years0.10 t_2 = 0.80 \implies t_2 = 8 \text{ years} 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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