Examveda

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

A. $$1\frac{1}{3}$$ years

B. $$1\frac{1}{2}$$ years

C. $$2\frac{1}{3}$$ years

D. $$2\frac{1}{2}$$ years

\eqalign{ & {\text{Let the time be }}n{\text{ year}} \cr & {\text{Then,}} \cr & {\text{800}} \times {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = 926.10 \cr & \Leftrightarrow {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = \frac{{9261}}{{8000}} \cr & \Leftrightarrow {\left( {\frac{{21}}{{20}}} \right)^{2n}} = {\left( {\frac{{21}}{{20}}} \right)^3} \cr & \Leftrightarrow 2n = 3 \cr & \Leftrightarrow n = \frac{3}{2} \cr & \therefore n = 1\frac{1}{2}{\text{years}} \cr}