Question

Find the compound interest on 25000 RS at the rate of 12 percent per annum for three years

Answer 1

Explanation:

Compound Interest for 3 years on 25000 ruppees at rate of 12%p.a. =>

$25000((1 + \frac{12}{100})^{3} - 1) =$

$25000( {1.12}^{3} - 1) = 25000(1.728 - 1)$

$= 25000(0.728) = 18200 \: ruppees$

Hope it helps you.

Answer 2

Answer:

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

• $\longrightarrow$ Principle = Rs.25000
• $\longrightarrow$ Rate of Interest = 12 per annum
• $\longrightarrow$ Time = 3 years

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

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

• $\longrightarrow$ Compound Interest

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Concept :}}}}}}\end{gathered}$

★ Here we have given that the Principal is Rs.25000, Time is 3 years and rate is 15 per annum. As we know that to find the compound interest we need Amount. So firstly we will find out the amount.

★ After finding the amount we will find out the Compound interest by substituting the values in the formula.

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

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

$\pink{\underline{\boxed{\bf{A={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\purple{\underline{\boxed{\bf{C.I= A - P }}}}$

Where

• $\longrightarrow$ A = Amount
• $\longrightarrow$ P = Principle
• $\longrightarrow$ R = Rate of Interest
• $\longrightarrow$ T = Time
• $\longrightarrow$ C.I = Compound Interest

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

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

★ Let us find out the Amount by Substituting the values in the formula :

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

• Substituting the values

$\dashrightarrow{\sf{Amount={25000{\bigg(1 + \dfrac{12}{100}{\bigg)}^{3}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{(1 \times 100) + 12}{100}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{100 + 12}{100}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{112}{100}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \cancel{\dfrac{112}{100}}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{56}{50}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \cancel{\dfrac{56}{50}}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{28}{25}{\bigg)}^{3}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{28}{25} \times \dfrac{28}{25} \times \dfrac{28}{25}{\bigg)}}}}}}$

${\dashrightarrow{\sf{Amount={25000{\bigg( \dfrac{21952}{15625}{\bigg)}}}}}}$

${\dashrightarrow{\sf{Amount={25000 \times \dfrac{21952}{15625}}}}}$

${\dashrightarrow{\sf{Amount={\dfrac{25000 \times 21952}{15625}}}}}$

${\dashrightarrow{\sf{Amount={\dfrac{548800000}{15625}}}}}$

${\dashrightarrow{\sf{Amount={ \cancel{\dfrac{548800000}{15625}}}}}}$

${\dashrightarrow{\sf{Amount=Rs.35123.2}}}$

$\bigstar{\green{\underline{\boxed{\bf{Amount=Rs.35123.2}}}}}$

∴ The amonut is Rs.35123.2.

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

★ Now, Let us find out the compound interest by substituting the values in the formula :

$\dashrightarrow{\sf{Compound \: Interest= A - P }}$

• Substituting the values

${\dashrightarrow{\sf{Compound \: Interest= 35123.2 - 25000 }}}$

${\dashrightarrow{\sf{Compound \: Interest=Rs.10123.2 }}}$

$\bigstar{\orange{\underline{\boxed{\bf{Compound \: Interest=Rs.10123.2 }}}}}$

∴ The compound interest is Rs.10123.2.

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

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

$\small\red{\underline{\boxed{\bf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}$

$\small\red{\underline{\boxed{\bf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\small\red{\underline{\boxed{\bf{Amount = Principle + Interest}}}}$

$\small\red{\underline{\boxed{\bf{ Principle=Amount - Interest }}}}$

$\small\red{\underline{\boxed{\bf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

$\small\red{\underline{\boxed{\bf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

$\small\red{\underline{\boxed{\bf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}$

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