Question

find the amount and the compound interest on 25000 for 3 years at 4% p.a compounded annually

Answer 1

Amount = P(1+R/100)n

Amount = 25000(1+4/100)³

Amount = 25000(1+1/25)³

Amount = 25000(2/25)³

Amount = 2000

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Answer 2

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

Given that,

Principal, p = Rs 25000

Rate of interest, r = 4 % per annum compounded annually

Time, n = 3 years

We know,

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

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

On substituting the values, we get

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{4}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{1}{25} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{25 + 1}{25} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{26}{25} \bigg]}^{3}$

$\rm\implies \:\boxed{\tt{ \: \: Amount \: = \: Rs \: 28121.60 \: \: }}$

Now, We know that,

Compound Interest on a certain sum of money is given by

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

So, on substituting the values, we get

$\rm :\longmapsto\:Compound \: Interest = 28121.6 - 25000$

$\rm\implies \:\boxed{\tt{ \: \: Compound \: Interest \: = \: Rs \: 3121.60 \: }}$

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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 semi - annually for n years is given by

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

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

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

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

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