Mathematics of FinanceMCQMTP June 24 Series IIQuestion 1413 of 512
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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 a16 years

All Options:

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

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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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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