Mathematics for FinanceMTP 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.

Options

A10\displaystyle 10 years
B12\displaystyle 12 years
C13\displaystyle 13 years
D14\displaystyle 14 years
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Correct Answer

✅ Option b — 12\displaystyle 12 years

All Options:

  • A10\displaystyle 10 years
  • B12\displaystyle 12 years
  • C13\displaystyle 13 years
  • D14\displaystyle 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 = \frac{\ln(2)}{\ln(1.06)} Using log values: ln⁡(2)≈0.693147\ln(2) \approx 0.693147 ln⁡(1.06)≈0.058269\ln(1.06) \approx 0.058269 t=0.6931470.058269≈11.90 years≈12 yearst = \frac{0.693147}{0.058269} \approx 11.90 \text{ years} \approx 12 \text{ years} Hence, **Option B** is the correct answer.

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