question_answer 1)

                Vasudeuan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get (i) after 6 months? (ii) after 1 year?

Answer:

                (i) After 6 months P = Rs 60,000 R = 12% per annum \[=\frac{1}{2}\times 12%\] per half year    = 6% per half year           \[n=1\] half year               \[\therefore \]  \[A=P{{\left( 1+\frac{R}{100} \right)}^{n}}\] \[=60,\,000{{\left( 1+\frac{6}{100} \right)}^{1}}\] \[=60,000\times \frac{106}{100}\,\]= Rs 63, 600 Hence, he would get Rs 63,600 after 6 months.                                  (ii) After 1 year                   P = Rs 60,000                 R = 12% per annum          \[=\frac{12}{2}%\] per half year = 6% per half year \[n=1\] year \[=1\times 2\] half years = 2 half years \[\therefore \]  \[A=P\,{{\left( 1+\frac{R}{100} \right)}^{n}}\] \[=60,000{{\left( 1+\frac{6}{100} \right)}^{2}}\] \[=60,000{{\left( 1+\frac{3}{50} \right)}^{2}}\] \[=60,000{{\left( \frac{53}{50} \right)}^{2}}\] \[=60,000\times \,\frac{53}{50}\,\times \frac{53}{50}\] = Rs 67,416 Hence, he would get Rs 67,416 after 1 year.