Question

The compound interest on 1000 at 10% p.a. compounded annually for 2 years is​

Answer 1

Answer :-

• The compound interest is 210.

To find :-

• The compound interest.

Step-by-step explanation :-

• Before finding the compound interest, let's find the amount!

We know that :-

$\underline{ \boxed{\rm Amount = Principal \left(1 + \dfrac{Rate}{100} \right)^{Time} }}$

Here,

• Principal = 1000.
• Rate = 10% p.a.
• Time = 2 years.

Therefore,

$\longrightarrow\sf Amount = 1000 \left(1 + \dfrac{1\!\!\!\not0}{10\!\!\!\not0} \right)^{2}$

$\longrightarrow\sf Amount = 1000 \left( 1 + \dfrac{1}{10} \right)^{2}$

$\longrightarrow\sf Amount = 1000 \left( \dfrac{1 \times 10 + 1 \times 1}{10} \right)^{2}$

$\longrightarrow\sf Amount = 1000 \left( \dfrac{10 + 1}{10} \right)^{2}$

$\longrightarrow\sf Amount = 1000 \left( \dfrac{11}{10} \right)^{2}$

$\longrightarrow\sf Amount = 1000 \times \dfrac{11}{10} \times \dfrac{11}{10}$

$\longrightarrow\sf Amount = \cancel{\dfrac{1210000}{100}}$

$\longrightarrow\sf Amount = 1210$

-----------------------------------------------------------

• Now, let's find the compound interest!

We know that :-

$\underline{ \boxed{\rm CI = Amount - Principal}}$

Where,

• CI = Compound Interest.

Here,

• Amount = 1210.
• Principal = 1000.

Therefore,

$\dashrightarrow\bf CI = 1210 - 1000$

$\dashrightarrow\bf CI = 210$

Hence :-

• The compound interest is 210.

_____________________________

Answer 2

Answer:

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}\end{gathered}$

• ➳ Principal = Rs.1000
• ➳ Rate of Interest = 10% p.a.
• ➳ Time = 2 years

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{To Find :}}}}}}\end{gathered}$

• ➳ Compound Interest

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Using Formulae :}}}}}}\end{gathered}$

$\quad{\dag{\underline{\boxed{\sf{A={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\quad\dag{\underline{\boxed{\sf{C.I= A - P }}}}$

Where

• ➽ A = Amount
• ➽ P = Principle
• ➽ R = Rate of Interest
• ➽ T = Time Period
• ➽ C.I = Compound Interest

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\end{gathered}$

${\bigstar \:{\underline{\underline{\pmb{\frak{{Firstly, calculating\: the \: Amount.. }}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

• Substituting the values

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg(1 + \dfrac{10}{100}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{(1 \times 100) + 10}{100}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{100 + 10}{100}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{110}{100}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg(\cancel{\dfrac{110}{100}}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{55}{50}{\bigg)}^{2}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{55}{50} \times \dfrac{55}{50}{\bigg)}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000{\bigg( \dfrac{3025}{2500}{\bigg)}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {1000 \times \dfrac{3025}{2500}}}}}$

$\quad {: \longmapsto{\sf{Amount = {\dfrac{1000 \times 3025}{2500}}}}}$

$\quad {: \longmapsto{\sf{Amount = {\dfrac{3025000}{2500}}}}}$

$\quad {: \longmapsto{\sf{Amount = {\cancel{\dfrac{3025000}{2500}}}}}}$

$\quad {: \longmapsto{\sf{Amount = {Rs.1210}}}}$

$\quad\dag{\underline{\boxed{\sf{\purple{Amount = {Rs.1210}}}}}}$

$\begin{gathered}\end{gathered}$

${\bigstar{\underline{\underline{\pmb{\frak{Now,Finding \: the \: Compound \: Interest}}}}}}$

$\quad{: \longmapsto{\sf{Compound \: Interest = {Amount - Principle }}}}$

• Substituting the values

$\quad{: \longmapsto{\sf{Compound \: Interest = {1210 - 1000 }}}}$

$\quad{ : \longmapsto{\sf{Compound \: Interest = {210 }}}}$

$\quad{\dag{\underline{\boxed{\sf{\purple{Compound \: Interest = {Rs.210}}}}}}}$

• Hence, The Compound Interest is Rs.210.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Learn More :}}}}}}\end{gathered}$

$\quad\dag{\underline{\boxed{\sf{\red{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\quad\dag{\underline{\boxed{\sf{\red{Amount = Principle + Interest}}}}}$

$\quad\dag{\underline{\boxed{\sf{\red{ P=Amount - Interest }}}}}$

$\quad\dag{\underline{\boxed{\sf{\red{ S.I = \dfrac{P \times R \times T}{100}}}}}}$

$\quad\dag{\underline{\boxed{\sf{\red{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}}$

$\quad\dag{\underline{\boxed{\sf{\red{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬