Find the simple interest and the amount when principal $ = $Rs.\[6400\] , rate $ = $\[6\% \] p.a. and time $ = $\[2\] years.

Hint: To calculate S.I and amount, we use the formula of S.I to get interest and then using interest, we calculate the sum on the given principal.

Formula used: \[S.I = \dfrac{{P \times R \times T}}{{100}}\] ,
\[\begin{array}{*{20}{l}}
  {P = Principal,} \\
  {R = Rate{\text{ }} of {\text{ }}interest,} \\
  {T = time}
\end{array}\]

Complete step by step answer:
As given,
Principal \[\left( P \right) = 6400\]
Rate \[\left( R \right) = 6\% {\text{ }}p.a.\]
Time \[\left( T \right) = 2{\text{ }} years\]
(1) Let interest be the S.I on the given principal amount of Rs. \[6400\]
∴ by S.I formula, we have
\[S.I = \dfrac{{P \times R \times T}}{{100}}\]
Where P is principal, R is rate per annum. T is time.
(2) Using values of P, R and T in the formula mentioned in step \[1\] to get S.I.
\[S.I = 6400 \times \dfrac{6}{{100}} \times 2\]
\[ = 64 \times 6 \times 2\]
\[ = 64 \times 12\]
\[S.I = Rs.768\]
(3) Hence interest on Rs.\[6400\] for $2$ years at 6% p.a. is Rs.\[768.\]
(4) Now to calculate the amount. We know that amount that a person receives after $2$ years on Rs.\[6400\] at 6% will be the sum of principal and interest on it.
\[\therefore A = P + I\]
Using value of \[P = {\text{ }}6400,\,\,\;S.I = Rs.768\]
\[ \Rightarrow A = 6400 + 768\]
\[ = Rs.7168\]

Additional Information: Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.

Note: In case if time is either in months or days then we convert it first in year after dividing by $12$ months or \[365\] days as rate is given in per annum.