Sita deposited Rs. 5000 at 10% simple interest for 2 yr. How much more money will Sita have in her account at the end of 2 yr, if it is compounded semi-annually? [SSC (CGL) 2012] |
A) Rs. 50
B) Rs. 40
C) Rs. 77.50
D) Rs. 85.50
Correct Answer: C
Solution :
Given, for simple interest |
Rate = 10%, Time = 2yr, |
Principal = 5000 |
We know that, |
\[\text{Simple}\,\,\text{interest}=\frac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] |
\[\Rightarrow \] \[\text{SI}=\frac{5000\times 10\times 2}{100}=\text{Rs}\text{.}\,\,1000\] (i) |
and for compound interest, |
Rate = 10% yearly or 5% half-yearly |
Time = 2 yr or 4 half years |
P = Rs. 5000 |
When the interest is compounded half-yearly, then the rate of interest is halved because it is compounded twice a year and time taken becomes twice of the original time. |
We know that, |
\[CI=P\left[ {{\left( 1+\frac{r}{100} \right)}^{t}}-1 \right]=5000\left[ {{\left( 1+\frac{5}{100} \right)}^{4}}-1 \right]\] |
\[\Rightarrow \]\[CI=5000\left[ \frac{194481}{160000}-1 \right]\] |
\[\Rightarrow \]\[CI=\frac{5000\times 34481}{160000}=Rs.\,\,1077.5\]...(ii) |
\[\therefore \]Required difference \[=CI-SI\] |
\[=1077.5-1000=Rs.\,\,77.5\] |
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