Mathematics for FinanceMTP Mar 22Question 1352 of 512
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In how many years will a sum of money become double at 5%\displaystyle 5\% p.a compound interest

Options

A14\displaystyle 14 years
B15\displaystyle 15 years
C16\displaystyle 16 years
D14.3\displaystyle 14.3 years
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Correct Answer

✅ Option d — 14.3\displaystyle 14.3 years

All Options:

  • A14\displaystyle 14 years
  • B15\displaystyle 15 years
  • C16\displaystyle 16 years
  • D14.3\displaystyle 14.3 years

Detailed Solution & Explanation

**Derivation of Doubling Time under Compound Interest** Given: - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum compounded annually - Let the sum be P\displaystyle P. Amount (A\displaystyle A) = 2P\displaystyle 2P **Step 1: Set up the compound interest equation** A=P(1+r)tA = P(1 + r)^t 2P=P(1.05)t2P = P(1.05)^t 2=(1.05)t2 = (1.05)^t **Step 2: Solve for t\displaystyle t using logarithms** ln⁡(2)=tln⁡(1.05)\ln(2) = t \ln(1.05) t=ln⁡(2)ln⁡(1.05)t = \frac{\ln(2)}{\ln(1.05)} Using log values: ln⁡(2)≈0.693147\ln(2) \approx 0.693147 ln⁡(1.05)≈0.048790\ln(1.05) \approx 0.048790 t=0.6931470.048790≈14.21 years≈14.3 yearst = \frac{0.693147}{0.048790} \approx 14.21 \text{ years} \approx 14.3 \text{ years} *(Note: The database lists Option C (16\displaystyle 16 years) as correct, which is a textbook discrepancy. The mathematically closest option is Option D.)* Hence, **Option D** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

More Questions from Mathematics for Finance

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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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