Mathematics of FinanceMCQMTP May 18Question 1271 of 512
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The time in which a sum of money will be doubled at 6%\displaystyle 6\% compound interest compounded interest compounded interest compounded annually approximately.

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

✅ Option b — $12$ years

All Options:

  • A$10$ years
  • B$12$ years
  • C$13$ years
  • D$14$ years

Detailed Solution & Explanation

**Derivation of Doubling Time under Compound Interest** Given: - Rate of Interest (r\displaystyle r) = 6%\displaystyle 6\% per annum compounded annually - Let the sum be P\displaystyle P. We want the amount to double (A=2P\displaystyle A = 2P). **Step 1: Set up the compound interest equation** A=P(1+r)tA = P(1 + r)^t 2P=P(1.06)t2P = P(1.06)^t 2=(1.06)t2 = (1.06)^t **Step 2: Solve for t\displaystyle t using logarithms** ln⁡(2)=tln⁡(1.06)\ln(2) = t \ln(1.06) t=ln⁡(2)ln⁡(1.06)t = ln⁡(2)ln⁡(1.06)\displaystyle \frac{\ln(2)}{\ln(1.06)} Using log values: ln⁡(2)≈0.693147\ln(2) ≈\displaystyle \approx 0.693147 ln⁡(1.06)≈0.058269\ln(1.06) ≈\displaystyle \approx 0.058269 t=0.6931470.058269≈11.90 years≈12 yearst = 0.6931470.058269\displaystyle \frac{0.693147}{0.058269} ≈\displaystyle \approx 11.90  years\displaystyle \text{ years} ≈\displaystyle \approx 12  years\displaystyle \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.

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

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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More Questions from Mathematics of Finance

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A certain sum of money was put at S.I. for $2.5$ years at a certain rate of S.I. p.a. Had it been put at $4\%$ higher rate, it would have fetched $500$ more. Find the sum of money.

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If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

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