Question:medium

A certain sum of money becomes 625/256 times of itself in 1 year. Find the rate of interest per annum if interest is compounded quarterly?

Updated On: Jan 15, 2026
  • 5
  • 25
  • 50
  • 100
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The Correct Option is D

Solution and Explanation

The compound interest formula is \( A = P \left(1 + \frac{r}{n}\right)^{nt} \). \( A \) represents the final amount, \( P \) the principal, \( r \) the annual interest rate, \( n \) the compounding frequency per year, and \( t \) the time in years. Given that the amount becomes \( \frac{625}{256} \) times the principal in 1 year with quarterly compounding (\( n = 4 \)), we substitute these values: \( \frac{625}{256}P = P \left(1 + \frac{r}{4}\right)^{4 \cdot 1} \). Simplifying yields \( \frac{625}{256} = \left(1 + \frac{r}{4}\right)^4 \). Taking the fourth root of both sides: \( \sqrt[4]{\frac{625}{256}} = 1 + \frac{r}{4} \), which simplifies to \( \frac{5}{4} = 1 + \frac{r}{4} \). Solving for \( r \): \( \frac{1}{4} = \frac{r}{4} \), leading to \( 1 = r \). Therefore, the annual interest rate is 100%. The answer is 100%, corresponding to option: 100.

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