Mathematics for FinancePYQ Dec 21Question 1231 of 512
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An amount is lent at R%\displaystyle R\% simple interest for R\displaystyle R years and the simple interest amount was one-fourth of the principal amount. Then R\displaystyle R is

Options

A5\displaystyle 5
B6\displaystyle 6
C512\displaystyle 5^{\frac{1}{2}}
D612\displaystyle 6^{\frac{1}{2}}
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Correct Answer

✅ Option a — 5\displaystyle 5

All Options:

  • A5\displaystyle 5
  • B6\displaystyle 6
  • C512\displaystyle 5^{\frac{1}{2}}
  • D612\displaystyle 6^{\frac{1}{2}}

Detailed Solution & Explanation

**Derivation of Simple Interest Rate and Time** Given: - Simple Interest (SI\displaystyle SI) = 14P\displaystyle \frac{1}{4} P (where P\displaystyle P is the principal) - Time (T\displaystyle T) is equal to Rate (R\displaystyle R), so T=R\displaystyle T = R. **Step 1: Set up the Simple Interest formula** SI=P×R×T100SI = \frac{P \times R \times T}{100} 14P=P×R×R100\frac{1}{4} P = \frac{P \times R \times R}{100} 14=R2100\frac{1}{4} = \frac{R^2}{100} **Step 2: Solve for R\displaystyle R** R2=1004=25R^2 = \frac{100}{4} = 25 R=25=5R = \sqrt{25} = 5 Hence, the interest rate is 5%\displaystyle 5\% and time is 5\displaystyle 5 years. Hence, **Option A** is the correct answer.

More Questions from Mathematics for Finance

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Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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