# In what time 8000 Rs. will amount to 9261 Rs. at 10% per annum compound interest, when the interest is compounded half yearly?

In what time 8000 Rs. will amount to 9261 Rs. at 10% per annum compound interest, when the interest is compounded half yearly?
[A]1.5 years
[B]2 years
[C]2.5 years
[D]3.5 years

1.5 years
Interest is compounded half yearly.
∴ Rate of interest = 5%
$Time = \frac{n}{2}\ years$
$\because A = P(1 + \frac{R}{100})^{T}$
$=> 9261 = 8000 (1 + \frac{5}{100})^{n}$
$=> \frac{9261}{8000} = (\frac{21}{20})^{n}$
$=> (\frac{21}{20})^{3} = (\frac{21}{20})^{n}$
$=> n = 3\ half\ years$
$= \frac{3}{2}\ years = 1\frac{1}{2}\ years$
Hence option [A] is correct answer.