Mathematics for FinanceMTP Dec 23 Series IQuestion 3947 of 507
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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 d — None 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

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=76−1=16≈0.1667 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.

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