question_answer 1)

                Find the amount which Ram will get on Rs 4,096, if he gave it for 18 months at \[12\frac{1}{2}%\] per annum, interest being compounded half yearly.

Answer:

                P = Rs 4,096 \[R=12\frac{1}{2}%\] per annum \[=\frac{25}{2}%\] per annum \[=\frac{1}{2}\times \frac{25}{2}%\] per half year \[n=18\] months \[=\frac{18}{6}\] half years = 3 half years. \[\therefore \]  \[A=P{{\left( 1+\frac{R}{100} \right)}^{n}}\] \[=4,096\,{{\left( 1+\frac{25}{4\times 100} \right)}^{3}}\] \[=4,096{{\left( 1+\frac{1}{16} \right)}^{3}}\] \[=4,096\,{{\left( \frac{17}{16} \right)}^{3}}\] \[=4,096\times \frac{17}{16}\times \frac{17}{16}\times \frac{17}{16}\] = Rs 4,913                 Hence, the required amount is Rs 4, 913.