Mathematics of FinancePYQ Jan 26Question 4204 of 507
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If a sum double itself in 8 years, then in how many years it will becomes four times, assuming that the simple interest is calculated.

Options

A16 years
B12 years
C24 years
D20 years
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Correct Answer

✅ Option c — 24 years

All Options:

  • A16 years
  • B12 years
  • C24 years
  • D20 years

Detailed Solution & Explanation

Let the principal amount be P\displaystyle P and the annual simple interest rate be r\displaystyle r (as a decimal).

Simple Interest formula:
I=P×r×tI = P \times r \times t
where I\displaystyle I is the interest earned and t\displaystyle t is the time in years. The total amount is:
A=P+I=P(1+rt)A = P + I = P(1 + rt)

**Case 1: The sum doubles itself in 8\displaystyle 8 years (t=8\displaystyle t = 8).**
The amount becomes 2P\displaystyle 2P, which means the interest earned I=2P−P=P\displaystyle I = 2P - P = P.
P=P×r×8P = P \times r \times 8
1=8r  ⟹  r=18=0.125 (or 12.5% per annum)1 = 8r \implies r = \frac{1}{8} = 0.125 \text{ (or } 12.5\% \text{ per annum)}

**Case 2: The sum becomes four times (A=4P\displaystyle A = 4P).**
The interest earned is I=4P−P=3P\displaystyle I = 4P - P = 3P. Let t′\displaystyle t' be the required number of years:
3P=P×r×t′3P = P \times r \times t'
3=r×t′3 = r \times t'

Substitute the value of r\displaystyle r from Case 1:
3=18×t′3 = \frac{1}{8} \times t'
t′=3×8=24 yearst' = 3 \times 8 = 24 \text{ years}

Hence, **Option C** 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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