| A sum of Rs. 11000 was taken as loan. This is to be repaid in two equal annual. If the rate of interest is 20% compounded annually, then the value of each instalments is |
A) Rs. 7500
B) Rs. 7000
C) Rs. 7100
D) Rs. 7200
Correct Answer: D
Solution :
| Given, \[r=20\]% |
| If a borrower pays the sum in parts, then he is paying in two instalments annually. |
| Let value of each be Rs. x. |
| Then,\[\frac{x}{1+\left( \frac{r}{100} \right)}+\frac{x}{{{\left( 1+\frac{r}{100} \right)}^{2}}}=11000\] |
| \[\Rightarrow \] \[\frac{x}{1+\frac{20}{100}}+\frac{x}{{{\left( 1+\frac{20}{100} \right)}^{2}}}=11000\] |
| \[\Rightarrow \] \[\frac{x}{\frac{6}{5}}+\frac{x}{\frac{36}{25}}=11000\] |
| \[\Rightarrow \] \[x\left( \frac{5}{6}+\frac{25}{36} \right)=11000\] |
| \[\Rightarrow \] \[x=\frac{11000\times 36}{55}\] |
| \[\Rightarrow \] \[x=\,\,\text{Rs}\text{. 7200}\] |
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