| sum of money doubles itself at compound interest in 15 yr. In how many years it will become eight times? |
A) 30
B) 45
C) 50
D) 60
Correct Answer: B
Solution :
| Let the sum be Rs. x. |
| Then, amount after \[15yr=2x\] |
| \[\Rightarrow \] \[2x=x{{\left( 1+\frac{r}{100} \right)}^{15}}\] |
| \[\Rightarrow \] \[2={{\left( 1+\frac{r}{100} \right)}^{15}}\] (i) |
| Let after n yr sum becomes eight times of itself. |
| Again, \[8x=x{{\left( 1+\frac{r}{100} \right)}^{n}}\] ... (ii) |
| \[\Rightarrow \] \[8={{\left( 1+\frac{r}{100} \right)}^{n}}\] |
| \[\Rightarrow \] \[{{(2)}^{3}}={{\left( 1+\frac{r}{100} \right)}^{n}}\] |
| \[\Rightarrow \] \[{{\left( 1+\frac{r}{100} \right)}^{3\times 15}}={{\left( 1+\frac{r}{100} \right)}^{n}}\] |
| \[\therefore \] \[n=45\,yr\] |
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