Mathematics of FinanceMCQPYQ Nov 18Question 1180 of 512
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A certain amount of money doubles itself in 10\displaystyle 10 years when deposited on simple interest. It would triple itself in

Options

A20\displaystyle 20 years
B15\displaystyle 15 years
C25\displaystyle 25 years
D30\displaystyle 30 years
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Correct Answer

✅ Option a — 20\displaystyle 20 years

All Options:

  • A20\displaystyle 20 years
  • B15\displaystyle 15 years
  • C25\displaystyle 25 years
  • D30\displaystyle 30 years

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Detailed Solution & Explanation

**Derivation of Time to Triple Principal under Simple Interest** Given: - Principal (P\displaystyle P) doubles itself in 10\displaystyle 10 years. **Step 1: Find the Rate of Interest (r\displaystyle r)** If the principal doubles, the Simple Interest (SI\displaystyle SI) earned is equal to the Principal (P\displaystyle P). SI=PSI = P t=10 yearst = 10 \text{ years} Using the Simple Interest formula: 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: Calculate the time (t2\displaystyle t_2) required to triple the principal** To triple the principal, the target Amount (A\displaystyle A) is 3P\displaystyle 3P. The required Simple Interest (SI2\displaystyle SI_2) is: SI2=A−P=3P−P=2PSI_2 = A - P = 3P - P = 2P Using the Simple Interest formula with r=10%\displaystyle r = 10\%: SI2=P×r×t2100SI_2 = \frac{P \times r \times t_2}{100} 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 A** 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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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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More Questions from Mathematics of Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

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.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

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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