Question

find the amount and compound interest on rs 5000 for 1 1/2years at 14 % per annum compounded half yearly


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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Principal, p = Rs 5000

Rate of interest, r = 14 % per annum compounded half yearly

Time, n = 3/2 years.

We know,

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded half yearly for n years is given by

$\purple{\rm :\longmapsto\: \boxed{\tt{ \: Amount = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n}}}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 5000 {\bigg[1 + \dfrac{14}{200} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 5000 {\bigg[1 + \dfrac{7}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 5000 {\bigg[ \dfrac{100 + 7}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 5000 {\bigg[ \dfrac{107}{100} \bigg]}^{3}$

$\rm\implies \:Amount \: = \: Rs \: 6125.21$

Now, We know that

$\purple{\boxed{\tt{ Compound \: Interest = Amount - Principal}}}$

So,

$\rm :\longmapsto\:Compound \: Interest = 6125.21 - 5000$

$\bf\implies \:Compound \: Interest \: = \: Rs \: 1125.21$

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MORE TO KNOW

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded yearly for n years is given by

$\purple{\rm :\longmapsto\: \boxed{\tt{ \: Amount = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n}}}}$

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded quarterly for n years is given by

$\purple{\rm :\longmapsto\: \boxed{\tt{ \: Amount = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n}}}}$

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded monthly for n years is given by

$\purple{\rm :\longmapsto\: \boxed{\tt{ \: Amount = p {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n}}}}$