Mathematics of FinanceMCQPYQ Jun 24Question 1476 of 512
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At 8%\displaystyle 8\% compounded annually, how long will it take $750$ to double?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — 9\displaystyle 9 years

All Options:

  • A$6.5$ years
  • B$48$ months
  • C9\displaystyle 9 years
  • D$12$ years

Detailed Solution & Explanation

To find how long it takes for a principal sum P\displaystyle P to double under compound interest, we use the compound interest formula: A=P(1+i)nA = P(1 + i)^n Given: * Future Amount (A\displaystyle A) = $2P$ * Interest rate (i\displaystyle i) = 8%\displaystyle 8\% p.a. = $0.08$ Substituting these values into the formula: 2P=P(1+0.08)n2P = P(1 + 0.08)^n 2=(1.08)n2 = (1.08)^n Taking natural logarithms on both sides: ln⁡(2)=nln⁡(1.08)\ln(2) = n \ln(1.08) 0.693147=n×0.0769610.693147 = n ×\displaystyle \times 0.076961 n=0.6931470.076961≈9.006 yearsn = 0.6931470.076961\displaystyle \frac{0.693147}{0.076961} ≈\displaystyle \approx 9.006  years\displaystyle \text{ years} Thus, it takes approximately 9\displaystyle 9 years for the investment to double. 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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