Mathematics for FinancePYQ May 19Question 1282 of 512
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A certain money doubles itself in 10\displaystyle 10 years when deposited on simple interest. It would triple itself in.

Options

A30\displaystyle 30 years
B20\displaystyle 20 years
C25\displaystyle 25 years
D15\displaystyle 15 years
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Correct Answer

✅ Option b — 20\displaystyle 20 years

All Options:

  • A30\displaystyle 30 years
  • B20\displaystyle 20 years
  • C25\displaystyle 25 years
  • D15\displaystyle 15 years

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 B** is the correct answer.

More Questions from Mathematics for Finance

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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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