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 \[=P{{\left( 1+\frac{R}{100} \right)}^{t}}\] |
\[\Rightarrow \]\[6760=x{{\left( 1+\frac{4}{100} \right)}^{2}}\]\[\Rightarrow \]\[x=\frac{6760}{{{\left( 1+\frac{1}{25} \right)}^{2}}}\] |
\[\Rightarrow \] \[x=\frac{6760\times 25\times 25}{26\times 26}=10\times 25\times 25\] |
\[\Rightarrow \] \[x=6250\] |
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