Mathematics of FinanceMCQMTP Nov 21Question 1330 of 512
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The sum of money doubles itself in 10\displaystyle 10 years. The number of years it would treble itself is:

Options

A25\displaystyle 25 years
B15\displaystyle 15 years
C20\displaystyle 20 years
DNone of these
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Correct Answer

✅ Option c — 20\displaystyle 20 years

All Options:

  • A25\displaystyle 25 years
  • B15\displaystyle 15 years
  • C20\displaystyle 20 years
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Time to Treble Sum under Simple Interest** Given: - A sum of money doubles itself in 10\displaystyle 10 years under Simple Interest. **Step 1: Find the rate of interest (r\displaystyle r)** If the sum doubles, the interest earned equals the principal (SI=P\displaystyle SI = P). SI=P×r×t100SI = \frac{P \times r \times t}{100} P=P×r×10100P = \frac{P \times r \times 10}{100} 1=r10  ⟹  r=10% per annum1 = \frac{r}{10} \implies r = 10\% \text{ per annum} **Step 2: Find time (t2\displaystyle t_2) to treble the sum (A=3P\displaystyle A = 3P)** The required simple interest is: SI2=A−P=3P−P=2PSI_2 = A - P = 3P - P = 2P Using the Simple Interest formula: 2P=P×10×t21002P = \frac{P \times 10 \times t_2}{100} 2=t210  ⟹  t2=20 years2 = \frac{t_2}{10} \implies t_2 = 20 \text{ years} 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

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

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

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