# A person invested a certain sum for five years at the rate of r% per annum simple interest. If he had invested the same sum at the same rate compounded half yearly for one year, he would have received the same amount. Find the value of r. Option 1) 1000% Option 2) 1600%          Option 3) 900%Option 4)    500% Option 5) 800%

R rishi raj

if amount of is same , then interest is also same

$S.I = C.I$

$\frac{PRT}{100} = P\left [ 1+\left \{ \frac{R/2}{100} \right \}^{2} \right ]$

$\frac{R}{20}+1 = \left \{ 1+\frac{R}{100} \right \}^{2}$
$\frac{1}{20}-\frac{1}{100}^{2}= \frac{R}{4000}$

$R= 1600$

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