Question : If Rs. 10000 amounts to Rs. 11664 invested in compound interest (compounded annually) for two years then the annual rate of compound interest is:
Option 1: 10%
Option 2: 9%
Option 3: 8%
Option 4: 6%
Correct Answer: 8%
Solution :
Principal ($P$) = Rs. 10000
Let the rate of Interest be $R$.
Time ($n$) = 2 years
$11664= P(1+\frac{R}{100})^{n} = 10000(1+\frac{R}{100})^{2}$
$(\frac{11664}{10000}) = (1+\frac{R}{100})^{2}$
$(\frac{108}{100})^{2} = (1+\frac{R}{100})^{2}$
$\frac{R}{100} = \frac{108}{100} - 1 = \frac{8}{100}$
$R = 8$%
Hence, the correct answer is 8%.
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