Q.If 5000 rupees becomes 5408 rupees in 2 years at a certain compound interest rate, determine the compound interest rate.

Let the interest rate be \( r\% \). \(\therefore\) According to the question, \[ 5000\left(1+\cfrac{r}{100}\right)^2 = 5408 \] \[ \left(1+\cfrac{r}{100}\right)^2 = \cfrac{5408}{5000} = \cfrac{676}{625} \] \[ \left(1+\cfrac{r}{100}\right)^2 = \left(\cfrac{26}{25}\right)^2 \] \[ 1+\cfrac{r}{100} = \cfrac{26}{25} \] \[ \cfrac{r}{100} = \cfrac{26}{25} - 1 = \cfrac{1}{25} \] \[ r = \cfrac{100}{25} = 4 \] \(\therefore\) The interest rate is \( 4\% \).
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