Mathematics for FinancePYQ Nov 20Question 1211 of 512
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The ratio of principal and the compound interest value for three years (compounded annually) is 216:127\displaystyle 216:127. The rate of interest is:

Options

A0.1777\displaystyle 0.1777
B0.1567\displaystyle 0.1567
C0.1666\displaystyle 0.1666
D0.1587\displaystyle 0.1587
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Correct Answer

✅ Option c — 0.1666\displaystyle 0.1666

All Options:

  • A0.1777\displaystyle 0.1777
  • B0.1567\displaystyle 0.1567
  • C0.1666\displaystyle 0.1666
  • D0.1587\displaystyle 0.1587

Detailed Solution & Explanation

**Derivation of Rate of Interest from Principal and CI Ratio** Given: - Ratio of Principal (P\displaystyle P) to Compound Interest (CI\displaystyle CI) for 3\displaystyle 3 years = 216:127\displaystyle 216:127 - Let P=216\displaystyle P = 216 and CI=127\displaystyle CI = 127. **Step 1: Calculate the future amount (A\displaystyle A)** A=P+CI=216+127=343A = P + CI = 216 + 127 = 343 **Step 2: Set up the Compound Interest Amount formula** A=P(1+r)tA = P(1 + r)^t 343=216(1+r)3343 = 216(1 + r)^3 343216=(1+r)3\frac{343}{216} = (1 + r)^3 **Step 3: Solve for r\displaystyle r** Observe that 343=73\displaystyle 343 = 7^3 and 216=63\displaystyle 216 = 6^3: (76)3=(1+r)3\left(\frac{7}{6}\right)^3 = (1 + r)^3 1+r=761 + r = \frac{7}{6} r=76−1=16≈0.1666 (or 16.66%)r = \frac{7}{6} - 1 = \frac{1}{6} \approx 0.1666 \text{ (or } 16.66\%\text{)} Hence, **Option C** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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