Question

Priyanka borrowed $ {\rm{Rs 8,000}} $ at $ 12\% $ simple interest for $ 3{\rm{ years}} $ and lent it to Renu for $ 3{\rm{ years}} $ at $ 15\% $ per annum compound interest, compounded annually, Priyanka’s profit at the end of $ 3{\rm{ years}} $ is
 $ {\rm{Rs}}\;2,880 $
 $ {\rm{Rs }}1,287 $
 $ {\rm{Rs }}4,167 $
None of these

Answer 1

Hint: The total amount she has paid to the borrowed one is equal to the product of principal amount and the time power of the sum of $ 1 $ and the rate. Then the compound interest will be equal to removing the total amount from the principal interest. Then she has lent the money to renu with simple interest. The formula to find the simple interest is equal to the ratio of product of principal interest, rate and time by $ 100 $ .

Complete step-by-step answer:
It is given that the principal amount is $ {\rm{Rs}}\;8000 $ .
Borrowed the money with $ 12\% $ simple interest.
The given time is $ 3{\rm{ years}} $ .
Lent has Renu for $ 3{\rm{ years}} $ .
Priyanka lent her money with a rate of $ 15\% $ per annum.
Hence to find the money Priyanka paid for the lender with interest is,
We know that the formula to find simple interest is,
 $ {\rm{SI}} = \dfrac{{{\rm{principle}} \times {\rm{rate}} \times {\rm{Time}}}}{{100}} $
Hence, substituting the principal amount, rate and time we will get the interest money which is paid by the Priyanka to the lender.
 $ \begin{array}{c}
{\rm{SI}} = \dfrac{{8000 \times 12 \times 3}}{{100}}\\
 = 2880
\end{array} $
Hence, the interest amount paid by Priyanka is $ {\rm{Rs}}\;2880 $ .
Now, Priyanka lent her money to Renu with $ 15\% $ compound interest. So, the find the total amount paid by Renu we use the formula,

 $ A = {\rm{principle}} \times {\left( {1 + \dfrac{{{\rm{rate}}}}{{100}}} \right)^{\rm{T}}} $
On substituting principle, rate and time in the above equation we get,
 $ \begin{array}{c}
A = 8000{\left( {1 + \dfrac{{15}}{{100}}} \right)^3}\\
 = 12167
\end{array} $
The total amount paid by Renu is $ {\rm{Rs}}\;12167 $ .
Now let us find the compound interest, the formula to find compound interest is $ {\rm{compound interest}} = {\rm{total amount}} - {\rm{principle amount}} $
On substitute the value of total amount and principal amount we get,
 $ \begin{array}{c}
{\rm{CI}} = {\rm{Rs}}\;12167 - {\rm{Rs}}\;8000\\
 = {\rm{Rs}}\;4167
\end{array} $
We know the formula to find the profit she get is,
 $ {\rm{gain}} = {\rm{CI}} - {\rm{SI}} $
On substituting the value for compound interest and simple interest we get,
 $ \begin{array}{c}
{\rm{gain}} = {\rm{Rs}}\;4167 - {\rm{Rs}}\;2880\\
 = {\rm{Rs}}\;1287
\end{array} $
The money Priyanka has gained is $ {\rm{Rs}}\;1287 $ .

Note: The compound interest is different from the simple interest. If the rate is given for compound interest use in compound interest and if the rate is used in simple interest use for simple interest only don’t get confused.