Mathematics for FinanceMTP June 24 Series IIQuestion 1413 of 512
All Questions

A sum of money, lent out at simple interest, doubles itself in 8 years. Find in how many years will the sum become 3 times itself.

Options

A16 years
B15 years
C20 years
DNone of these
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Correct Answer

✅ Option a — 16 years

All Options:

  • A16 years
  • B15 years
  • C20 years
  • DNone of these

Detailed Solution & Explanation

Let the principal be P\displaystyle P and the rate of simple interest be r%\displaystyle r\% p.a. The formula for simple interest is: SI=P×r×t100SI = \frac{P \times r \times t}{100} Given that the sum doubles itself in 8\displaystyle 8 years, the simple interest earned is equal to the principal: SI=P for t=8SI = P \text{ for } t = 8 P=P×r×8100P = \frac{P \times r \times 8}{100} 1=8r100  ⟹  r=1008=12.5% p.a.1 = \frac{8r}{100} \implies r = \frac{100}{8} = 12.5\% \text{ p.a.} We want to find the number of years t\displaystyle t for the sum to become 3\displaystyle 3 times itself, which means the interest earned will be 2P\displaystyle 2P: 2P=P×12.5×t1002P = \frac{P \times 12.5 \times t}{100} 2=0.125×t2 = 0.125 \times t Solving for t\displaystyle t: t=20.125=16 yearst = \frac{2}{0.125} = 16 \text{ years} Thus, the sum will become 3\displaystyle 3 times itself in 16\displaystyle 16 years. Hence, **Option A** is the correct answer.

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?

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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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