Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-43

A certain sum invested with interest of 8% per annum, compounded semi-annually amounts to Rs. 6760 at the end of 1 yr. The sum is                                                                                             [SSC (CPO) 2014]

A) Rs. 6000

B) Rs. 6520

C) Rs. 6250

D) Rs. 6500

Correct Answer: C

Solution :

Let the sum invested be Rs. x.

Amount at the end of 1 yr = Rs. 6760

Now, rate of interest = 8% and time duration is 1 yr.

Given, in the question that the amount is compounded semi-annually, i.e. half-yearly.

Hence, rate of interest changes to

\[\frac{R}{2}=\frac{8}{2}\]% =4%

and time duration becomes \[2t=2\times 1=2\,\,yr\]

By the formula of compound interest, we get

Amount \[=P{{\left( 1+\frac{R}{100} \right)}^{t}}\]

\[\Rightarrow \]\[6760=x{{\left( 1+\frac{4}{100} \right)}^{2}}\]\[\Rightarrow \]\[x=\frac{6760}{{{\left( 1+\frac{1}{25} \right)}^{2}}}\]

\[\Rightarrow \] \[x=\frac{6760\times 25\times 25}{26\times 26}=10\times 25\times 25\]

\[\Rightarrow \] \[x=6250\]