In how many years will a sum of Rs. 800 become Rs. 926.10 at 10% per annum compounded semi-annually?
Answer & explanation
Correct answer: option 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