| An amount at compound interest doubles itself in 4 yr. In how many years will the amount become 4 times itself? |
A) 8 yr
B) 12 yr
C) 16 yr
D) 24 yr
Correct Answer: A
Solution :
| Let Rs. P be the given sum of money. |
| We have \[2P=P{{\left( 1+\frac{R}{100} \right)}^{4}}\] |
| \[\Rightarrow \] \[2={{\left( 1+\frac{R}{100} \right)}^{4}}\] |
| \[\Rightarrow \] \[{{2}^{\frac{1}{4}}}=\left( 1+\frac{R}{100} \right)\] |
| Let the sum become 4 times in T yr. |
| Then, \[4P=P{{\left( 1+\frac{R}{100} \right)}^{T}}\] |
| \[\Rightarrow \] \[4={{\left( 1+\frac{R}{100} \right)}^{T}}\]\[\Rightarrow \]\[4={{\left( {{2}^{\frac{1}{4}}} \right)}^{T}}\] |
| \[\Rightarrow \] \[4={{2}^{\frac{T}{4}}}\]\[\Rightarrow \]\[{{2}^{2}}={{2}^{\frac{T}{4}}}\] |
| \[\Rightarrow \] \[T=4\times 2=8yr\] |
You need to login to perform this action.
You will be redirected in
3 sec
