Mathematics for FinanceMTP June 24 Series IIIQuestion 1422 of 512
All Questions

The time in which a sum of money will be doubled at 6%\displaystyle 6\% compound 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

Let the principal be P\displaystyle P. The rate of compound interest is r=6%\displaystyle r = 6\% p.a. compounded annually, so i=0.06\displaystyle i = 0.06. We want to find the approximate number of years (t\displaystyle t) for the sum to double (A=2P\displaystyle A = 2P): P(1+i)t=2PP(1+i)^t = 2P (1.06)t=2(1.06)^t = 2 Taking natural logarithms on both sides: tln⁡(1.06)=ln⁡(2)t \ln(1.06) = \ln(2) t≈0.6931470.058269≈11.9 yearst \approx \frac{0.693147}{0.058269} \approx 11.9 \text{ years} Thus, the approximate number of years is 12\displaystyle 12 years. Hence, **Option B** 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

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

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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