Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 3947 of 512
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The ratio of principal and the compounded interest value for three years (Compounded annually) is 216:127\displaystyle 216:127. The rate of interest is

Options

ARs.80,000\displaystyle 80,000
BRs.90,000\displaystyle 90,000
CRs.50,000\displaystyle 50,000
DNone of these
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Correct Answer

Option dNone of these

All Options:

  • ARs.80,000\displaystyle 80,000
  • BRs.90,000\displaystyle 90,000
  • CRs.50,000\displaystyle 50,000
  • DNone of these

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Detailed Solution & Explanation

Let the principal be P\displaystyle P and the compound interest be CI\displaystyle CI. The ratio of the principal to the compound interest for 3\displaystyle 3 years is given as: PCI=216127\frac{P}{CI} = \frac{216}{127} Let P=216x\displaystyle P = 216x and CI=127x\displaystyle CI = 127x. The total amount A\displaystyle A is: A=P+CI=216x+127x=343xA = P + CI = 216x + 127x = 343x The formula for the compound amount compounded annually is: A=P(1+i)3A = P(1+i)^3 where i\displaystyle i is the annual rate of interest. Substituting the values: 343x=216x(1+i)3343x = 216x(1+i)^3 (1+i)3=343216(1+i)^3 = \frac{343}{216} Since 343=73\displaystyle 343 = 7^3 and 216=63\displaystyle 216 = 6^3, we can rewrite this as: (1+i)3=(76)3(1+i)^3 = \left(\frac{7}{6}\right)^3 Taking the cube root on both sides: 1+i=761+i = \frac{7}{6} i=761=160.1667 or 16.67%i = \frac{7}{6} - 1 = \frac{1}{6} \approx 0.1667 \text{ or } 16.67\% Under the given option choices (which appear to be copied from another question by error), the correct rate of 16.67%\displaystyle 16.67\% is not listed. Hence, "None of these" is the mathematically correct choice under the listed options. Hence, **Option D** 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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