Mathematics for FinanceMTP June 24 Series IIIQuestion 1418 of 512
All Questions

In how many years will a sum of money double at 5%\displaystyle 5\% p.a compounded interest?

Options

A15 years 3 months
B14 years 2 months
C14 years 3 months
D15 years 3 months
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Correct Answer

✅ Option b — 14 years 2 months

All Options:

  • A15 years 3 months
  • B14 years 2 months
  • C14 years 3 months
  • D15 years 3 months

Detailed Solution & Explanation

Let the principal be P\displaystyle P and the compound interest rate be i=0.05\displaystyle i = 0.05 (5% p.a.). Under compound interest, the amount A\displaystyle A after t\displaystyle t years is: A=P(1+i)tA = P(1+i)^t We want to find the time t\displaystyle t for the sum of money to double itself (A=2P\displaystyle A = 2P): 2P=P(1.05)t  ⟹  (1.05)t=22P = P(1.05)^t \implies (1.05)^t = 2 Taking natural logarithms on both sides: tln⁡(1.05)=ln⁡(2)t \ln(1.05) = \ln(2) t≈0.6931470.048790≈14.207 yearst \approx \frac{0.693147}{0.048790} \approx 14.207 \text{ years} To convert the fractional part of years into months: Months=0.207×12≈2.48 months≈2 months\text{Months} = 0.207 \times 12 \approx 2.48 \text{ months} \approx 2 \text{ months} Thus, it takes approximately 14\displaystyle 14 years and 2\displaystyle 2 months for the sum of money to double. 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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