Question

Rajeev deposited Rd 20,000 in a bank where compound interest is computed 6% annually .how much amount he will get at the end of the 3rd year​

Answer 1

$\bf \underline{Given} :$ ↴

$\sf \implies Principal = Rs. \: 20000$

$\sf \implies Rate = 6 \: \%$

$\sf \implies Time = 3 \: Years$

$\bf \underline{To \: find} :$ ↴

$\sf \implies We \: have \: to \: find \: the \: amount.$

$\bf \underline{\underline{Solution}}$

$\sf \implies \boxed{ \pink{\sf{\: Amount = P \bigg( 1 + \dfrac{R }{100} \bigg)^{n}}}}$

$\sf Where,$

$\sf \underline{P = Principal}, \: \underline{R = Rate} \: and \: \underline{ n = Time}$

$\sf Putting \: the \: values,$

$\sf \implies Amount = 20000 \bigg( 1 + \dfrac{6 }{100} \bigg)^{3}$

$\sf \implies 20000 \bigg( 1 + \dfrac{3 }{50} \bigg)^{3}$

$\sf \implies 20000 \bigg( \dfrac{50 + 3 }{50} \bigg)^{3}$

$\sf \implies 20000 \bigg( \dfrac{53}{50} \bigg)^{3}$

$\sf \implies 20000 \times \dfrac{148877}{125000}$

$\sf \implies \dfrac{4 \times 148877}{25}$

$\sf \implies \dfrac{595508}{25}$

$\red{\sf \implies Rs. \: 23820.32}$

$\underline{ \boxed{ \pink{\sf \: Thus, amount = Rs. \: 23820.32}}}$

Answer 2

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Given:}}}}}}}\end{gathered}$

• $\dashrightarrow{\sf{Principle = 20000}}$
• $\dashrightarrow{\sf{Rate = 6\%}}$
• $\dashrightarrow\sf{Time = 3 \: years}$

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{To Find :}}}}}}}\end{gathered}$

• $\dashrightarrow{\sf{Amount}}$

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Using Formula :}}}}}}}\end{gathered}$

${\large\dag}{\underline{\sf{\boxed{\sf{Amount = P \bigg( 1 + \dfrac{R }{100} \bigg)^{n}}}}}}$

Where

• $\dashrightarrow{\sf{P = Principle}}$
• $\dashrightarrow{\sf{R = Rate}}$
• $\dashrightarrow{\sf{N = Time }}$

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Solution:}}}}}}}\end{gathered}$

$\quad{: \implies{\sf{Amount = \bf{ P \bigg( 1 + \dfrac{R }{100} \bigg)^{n}}}}}$

• Substituting the values

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( 1 + \dfrac{6 }{100} \bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( 1 \times 100 + \dfrac{6 }{100} \bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \dfrac{100 + 6 }{100} \bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \dfrac{106}{100} \bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \cancel{\dfrac{106}{100}}\bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \dfrac{53}{50} \bigg)^{3}}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \dfrac{53}{50} \times \dfrac{53}{50} \times \dfrac{53}{50} \bigg)}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \bigg( \dfrac{148877}{125000} \bigg)}}}}$

$\quad{: \implies{\sf{Amount = \bf{ 20000 \times \dfrac{148877}{125000}}}}}$

$\quad{: \implies{\sf{Amount = \bf{{\cancel{20000}} \times \dfrac{148877}{\cancel{125000}}}}}}$

$\quad{: \implies{\sf{Amount = \bf{{4} \times \dfrac{148877}{25}}}}}$

$\quad{: \implies{\sf{Amount = \bf \dfrac{595508}{25}}}}$

$\quad{: \implies{\sf{Amount = \bf {\cancel{\dfrac{595508}{25}}}}}}$

$\quad{: \implies{\sf{Amount = \bf{23820.32}}}}$

$\begin{gathered} \dag{\overline{\underline{\boxed{\textsf{\textbf{\color{red}{Amount = Rs.23820.32}}}}}}}\end{gathered}$

$\therefore {\underline{\sf{\pmb{The \: Amount \: is \: Rs.23820.32}}}}$

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Learn More:}}}}}}}\end{gathered}$

★ Formula of Simple Interest (S.I)

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

★ Formula of Principle(P) if Amount and Interest given

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

★ Formula of Principle (P) if Interest,time and rate given

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

★ Formula of Principle (P) if amount,time and rate given

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

★ Formula of Amount if Principle (P) and Interest (I) given

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