Question

find the amount and the compound intrest on rs.2000 at 10% p.a for 2 and half years, compounded annually.​

Answer 1

Step-by-step explanation:

Answer :-

We have,

• P = ₹2000
• R = 10%
• T = 2 years 6 months or 2.5 years

To Find :-

• Amount
• Compound Interest

Solution :-

$\sf \: Refer \: to \: the \: attachment \: \hearts$

Answer 2

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

Given that,

Principal, P = Rs 2000

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

Time, n = 2 1/2 year

We know,

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

$\boxed{\tt{Amount = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n}\bigg[1 + \dfrac{r}{100} \times \frac{m}{s} \bigg]}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 2000 {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}\bigg[1 + \dfrac{10}{100} \times\dfrac{1}{2}\bigg]$

$\rm :\longmapsto\:Amount = 2000 {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}\bigg[1 + \dfrac{1}{10} \times\dfrac{1}{2}\bigg]$

$\rm :\longmapsto\:Amount = 2000 {\bigg[\dfrac{10 + 1}{10} \bigg]}^{2}\bigg[1 + \dfrac{1}{20} \bigg]$

$\rm :\longmapsto\:Amount = 2000 {\bigg[\dfrac{11}{10} \bigg]}^{2}\bigg[\dfrac{20 + 1}{20} \bigg]$

$\rm :\longmapsto\:Amount = 2000 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{21}{20}$

$\bf\implies \:Amount = Rs \: 2541$

We know,

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

So, on substituting the values, we get

$\rm :\longmapsto\:Compound \: Interest = 2541 - 2000$

$\bf\implies \:Compound \: Interest = Rs \: 541$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \bf\implies \:\begin{cases} &\bf{Amount = Rs \: 2541} \\ \\ &\bf{Compound \: Interest = Rs \: 541} \end{cases}\end{gathered}\end{gathered}$

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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

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

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

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

3. 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

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