Question

Find the amount and Compound Interest for ₹100 at the rate of 10% compounded half yearly for 1/ 2 years.​

Answer 1

Answer:

10.25

Step-by-step explanation:

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Answer 2

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

Given that,

➢ Principal, P = ₹ 100

➢ Rate of interest, r = 10 % per annum compounded half yearly.

➢ Time, n = 1/2 year

We know,

Amount on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually 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

$\rm :\longmapsto\:Amount = 100 {\bigg[1 + \dfrac{10}{200} \bigg]}^{1}$

$\rm :\longmapsto\:Amount = 100 {\bigg[1 + \dfrac{1}{20} \bigg]}$

$\rm :\longmapsto\:Amount = 100 {\bigg[ \dfrac{20 + 1}{20} \bigg]}$

$\rm :\longmapsto\:Amount = 100 {\bigg[ \dfrac{21}{20} \bigg]}$

$\bf\implies \:Amount = 105$

Now, We know,

$\red{\rm :\longmapsto\: \sf{ \: Compound \: interest = Amount - Principal }}$

So,

$\rm :\longmapsto\:Compound \: interest = 105 - 100$

$\bf\implies \:Compound \: interest = 5$

So,

• Amount = ₹ 105

• Compound Interest = ₹ 5

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MORE TO KNOW

1. Amount on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

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

2. 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

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

3. 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

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