| The interest received on a sum of money when invested in scheme A is equal to the interest received on the same sum of money when invested for 2 yr in scheme B. Scheme A offers simple interest (per cent per annum) and scheme B offers compound interest (compounded annually). Both the scheme offers the same rate of interest. If the numerical value of the number of years for which the sum is invested in scheme A is same as the numerical value of the rate of interest offered by the same scheme, what is the rate of interest (per cent per annum) offered by scheme A? |
A) 3%
B) \[2\frac{1}{77}\]%
C) \[3\frac{4}{99}\]%
D) \[2\frac{2}{99}\]%
E) 2%
Correct Answer: D
Solution :
| Let principal = Rs. P, rate = R% |
| For scheme A, \[SI=\frac{P\times R\times T}{100}\] |
| \[SI=\frac{P\times R\times R}{100}=\frac{P{{R}^{2}}}{100}\] (i) |
| For scheme B, \[CI=P\left[ {{\left( 1+\frac{R}{100} \right)}^{2}}-1 \right]\] |
| \[CI=P\left[ \left( 1+\frac{{{R}^{2}}}{100\times 100}+\frac{2R}{100}-1 \right) \right]\] |
| \[=P\left[ \frac{{{R}^{2}}}{100\times 100}+\frac{R}{50} \right]\] |
| Now. equating Eqs. (i) and (ii), we have |
| \[R=\frac{200}{99}\]%\[\Rightarrow \]\[R=2\frac{2}{99}\]% |
You need to login to perform this action.
You will be redirected in
3 sec
