Question

Find the compound interest on rupees 15000 in 3 years at 5% per annum the interest being compounded half yearly

Answer 1

AnswEr :

C.I. = Rs.2395.4

$\bf{We\:have}\begin{cases}\rm{Principal,[P]=Rs.15000}\\ \rm{Rate,[R]=5\%}\\ \rm{Time,[T]=3years}\end{cases}}$

$\bf{\large{\underline{\underline{\rm{To\:finD\::}}}}}}$

The compound Interest according to half yearly.

$\bf{\Large{\underline{\underline{\tt{\red{Explanation\::}}}}}}$

Half yearly according to rate, we get;

$\leadsto\tt{Rate\:=\:\cancel{\dfrac{5}{2} }\%}\\\\\leadsto\tt{Rate\:=\:2.5\%}$

Half yearly according to time, we get;

$\leadsto\tt{Time\:=\:3\:years\times 2\:years}\\\\\leadsto\tt{Time\:=\:6\:years}$

$\bf{\large{\underline{\underline{\tt{\red{A.T.Q.\::}}}}}}$

Formula use :

$\bf{\large{\boxed{\rm{Amount\:(A)=Principal\:(P)\bigg(1+\frac{R}{100} \bigg)^{n} }}}}}}$

$\dashrightarrow\tt{A=15000\bigg(1+\cancel{\dfrac{2.5}{100} }\bigg)^{6} }\\\\\\\\\dashrightarrow\tt{A=15000\bigg(1+\dfrac{1}{40} \bigg)^{6} }\\\\\\\\\dashrightarrow\tt{A=15000\bigg(\dfrac{40+1}{40} \bigg)^{6} }\\\\\\\\\dashrightarrow\tt{A=15000*\bigg(\dfrac{41}{40} \bigg)^{6} }\\\\\\\\\dashrightarrow\tt{A=15\cancel{000}*\dfrac{41}{4\cancel{0}} *\dfrac{41}{4\cancel{0}} *\dfrac{41}{4\cancel{0}} *\dfrac{41}{40} *\dfrac{41}{40} *\dfrac{41}{40}}$

$\dashrightarrow\tt{A=\dfrac{15*41*41*41*41*41*41}{4*4*4*40*40*40} }\\\\\\\\\dashrightarrow\tt{A=\cancel{\dfrac{71251563615}{4096000} }}\\\\\\\\\dashrightarrow\tt{\red{A=Rs.17395.40}}$

Now,

$\Longrightarrow\rm{Compound\:Interest\:(C.I.)=A\:-\:P}\\\\\\\Longrightarrow\rm{Compound\:Interest\:(C.I.)=Rs.(17395.40\:-\:15000)}\\\\\\\Longrightarrow\rm{\red{Compound\:Interest\:(C.I.)=Rs.2395.4}}$

Answer 2

Answer

The answer is Rs.2395.40. Since the compounding half yearly, half yearly interest would be 2.50% ( 5%/2 ) and the number of periods is 6 ( 3*2 as there will be 6 half years in 3 years ) Using the formula FV = PV*(1+r)^n, the future value with interest is Rs.17395.40. After deducting the Principal of Rs.15000 compound interest is 2395.40