In how many years will a sum of Rs. 800 become Rs. 926.10 at 10% per annum compounded semi-annually?

$1\frac{1}{2}$

Interest is compounded semi - annually ,

So, Actual rate of interest = \(\frac{10}{2}\)% = 5%

The formula that we used here is :-

Amount = Principal × [ 1 + \(\frac{Rate}{100}\) ]^t

926.10 = 800 × [ 1 + \(\frac{5}{100}\) ]^t

926.10 = 800 × [ \(\frac{21}{20}\) ]^t

\(\frac{9261}{8000}\) = [ \(\frac{21}{20}\) ]^t

[ \(\frac{21}{20}\) ]³ = [ \(\frac{21}{20}\) ]^t

t = 3

As interest is compounded semi - annually.

So, Actual time = 1.5 years

Ans :- (B)  1\(\frac{1}{2}\) year