| 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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