Question

Find the difference between simple interest
& compound interest on rs 30000 for
3 years at 10% per annum, when the
interest is compounded annually​

Answer 1

Answer:

HERE IS YOUR ANSWER MATE

Step-by-step explanation:

PRINCIPAL=30000

TIME =3 YEARS

RATE= 10%P.A

30000×3×10/100=9000

THEREFORE WE HAVE TO MINUS S.I-CI

S.I= 30000

C.I=9000

=S.I -C.I=21000

Answer 2

Answer:

${\large{\underline{\underline{\pmb{\frak{Given:-}}}}}}$

• ★ Principle = Rs.30000
• ★ Time = 3 years
• ★ Rate of Interest = 10%

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

${\large{\underline{\underline{\pmb{\frak{To \: Find:-}}}}}}$

• ★ Simple Interest
• ★ Amount
• ★ Compound Interest
• ★ Difference between simple interest and compound interest

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

${\large{\underline{\underline{\pmb{\frak{Using \: Formulae:-}}}}}}$

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

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

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

$\quad\bigstar{\underline{\boxed{\sf{Difference = S.I - C.I}}}}$

Where

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

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

${\large{\underline{\underline{\pmb{\frak{Solution:-}}}}}}$

$\red\bigstar$ Calculating the Simple Interest :-

$\quad{\dashrightarrow{\sf{ S.I=\dfrac{P \times R \times T}{100}}}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{ S.I=\dfrac{30000\times 10\times 3}{100}}}}$

$\quad{\dashrightarrow{\sf{ S.I=\dfrac{30000\times 30}{100}}}}$

$\quad{\dashrightarrow{\sf{ S.I=\dfrac{900000}{100}}}}$

$\quad{\dashrightarrow{\sf{ S.I= \cancel\dfrac{900000}{100}}}}$

$\quad{\dashrightarrow{\sf{ S.I=Rs.9000}}}$

$\quad\bigstar\underline{\boxed{\sf{\purple{ Simple \: Interest=Rs.9000}}}}$

∴ The Simple Interest is Rs.9000.

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

$\red\bigstar$ Calculating the Amount :-

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

• Substuting the values

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg(1 + \dfrac{10}{100}{\bigg)}^{3}}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg(1 + \cancel\dfrac{10}{100}{\bigg)}^{3}}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg(1 + \dfrac{1}{10}{\bigg)}^{3}}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg( \dfrac{(1 \times 10) + 1}{10}{\bigg)}^{3}}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg( \dfrac{10 + 1}{10} \bigg)}^{3}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg( \dfrac{11}{10} \bigg)}^{3}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg( \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \bigg)}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000{\bigg( \dfrac{1331}{1000} \bigg)}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30000 \times \dfrac{1331}{1000}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={\cancel{30000} \times \dfrac{1331}{\cancel{1000}}}}}}$

$\quad{\dashrightarrow{\sf{Amount ={30\times 1331}}}}$

$\quad{\dashrightarrow{\sf{Amount ={Rs.39930}}}}$

$\quad\bigstar{\underline{\boxed{\sf{\purple{Amount ={Rs.39930}}}}}}$

∴ The Amount is Rs.39930.

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

$\red\bigstar$ Calculating the compound interest :-

$\quad{\dashrightarrow{\sf{C.I= A - P }}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{C.I=39930- 30000 }}}$

$\quad{\dashrightarrow{\sf{C.I=9930 }}}$

$\quad{\bigstar\underline{\boxed{\sf{\purple{C.I=9930 }}}}}$

∴ The Compound interest is Rs.9930

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

$\red\bigstar$ Now, Finding the difference between simple interest and compound interest :-

$\quad{\dashrightarrow{\sf{Difference = C.I - S.I}}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{Difference =9930 - 9000}}}$

$\quad{\dashrightarrow{\sf{Difference =Rs.930}}}$

$\quad\bigstar{\underline{\boxed{\sf{\purple{Difference =Rs.930}}}}}$

∴ The difference between simple interest & compound interest is Rs.930.

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

${\large{\underline{\underline{\pmb{\frak{Answer:-}}}}}}$

• ★ The Simple Interest is Rs.9000
• ★ The Amount is Rs.39930
• ★ The Compound interest is Rs.9930
• ★ The difference between simple interest & compound interest is Rs.930

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

${\large{\underline{\underline{\pmb{\frak{Learn \: More:-}}}}}}$

$\red\bigstar$ More Userful Formulas :-

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

$\quad{\dashrightarrow{\sf{Amount = Principle + Interest}}}$

$\quad{\dashrightarrow{\sf{ P=Amount - Interest }}}$

$\quad{\dashrightarrow{\sf{ S.I = \dfrac{P \times R \times T}{100}}}}$

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

$\quad{\dashrightarrow{\sf{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}$

$\quad{\dashrightarrow{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}$

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