Question

What amount is to be repaid on a loan of Rs.12000 for 2 years at 10% per annum compounded annually. Also find Compound interest. steps

Answer 1

Answer:

2400

$12000 \div 10 \\ = 1200 \\ = 1200 \times 2 = 2400 \: rs$

Answer 2

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

Principal, p = Rs 12000

Rate of interest, r = 10 % per annum compounded annually

Time period, n = 2 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

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

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 12000 {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 12000 {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 12000 {\bigg[ \dfrac{10 + 1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 12000 {\bigg[ \dfrac{11}{10} \bigg]}^{2}$

$\rm\implies \: \boxed{\tt{ \:Amount \: = \:Rs \: 14520 \: }}$

Now, We know that

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

So, on substituting the values, we get

$\rm :\longmapsto\:Compound \: interest = 14520 - 10000$

$\rm\implies \:\boxed{\tt{ \: Compound \: interest \: = \: Rs \: 4520 \: }}$

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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

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

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

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

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

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