Mathematics for FinancePYQ May 20Question 1302 of 512
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The time by which a sum of money would treble itself at 8%\displaystyle 8\% p.a. C. I. is

Options

A14.28\displaystyle 14.28 years
B14\displaystyle 14 years
C12\displaystyle 12 years
Dnone of these
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Correct Answer

✅ Option a — 14.28\displaystyle 14.28 years

All Options:

  • A14.28\displaystyle 14.28 years
  • B14\displaystyle 14 years
  • C12\displaystyle 12 years
  • Dnone of these

Detailed Solution & Explanation

**Derivation of Trebling Time under Compound Interest** Given: - Rate of Interest (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded annually - Let the principal be P\displaystyle P. We want the amount to treble (A=3P\displaystyle A = 3P). **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 3P=P(1+0.08)t3P = P(1 + 0.08)^t 3=(1.08)t3 = (1.08)^t **Step 2: Solve for t\displaystyle t using logarithms** ln⁡(3)=tln⁡(1.08)\ln(3) = t \ln(1.08) t=ln⁡(3)ln⁡(1.08)t = \frac{\ln(3)}{\ln(1.08)} Using log values: ln⁡(3)≈1.098612\ln(3) \approx 1.098612 ln⁡(1.08)≈0.076961\ln(1.08) \approx 0.076961 t=1.0986120.076961≈14.28 yearst = \frac{1.098612}{0.076961} \approx 14.28 \text{ years} Hence, **Option A** is the correct answer.

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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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