Question

WHAT IS THE DIFFERENCE BETWEEN SIMPLE AND COMPOUND INTEREST ON ₹7300 AT THE RATE OF 6% PER ANNUM IN 2 YEARS​

Answer 1

Answer:

Given :-

• A sum on Rs 7300 at the rate of 6% per annum in 2 years.

To Find :-

• What is the difference between the simple interest and compound interest.

Solution :-

First, we have to find the simple interest :

As we know that :

$\bigstar$ Simple Interest or S.I Formula :

$\mapsto \sf\boxed{\bold{\pink{S.I =\: \dfrac{PRT}{100}}}}$

where,

• S.I = Simple Interest
• P = Principal
• R = Rate of Interest
• T = Time Period

Given :

• Principal = Rs 7300
• Rate of Interest = 6% p.a.
• Time Period = 2 years

According to the question by using the formula we get,

$\implies \sf S.I =\: \dfrac{7300 \times 6 \times 2}{100}$

$\implies \sf S.I =\: \dfrac{876\cancel{00}}{1\cancel{00}}$

$\implies \sf\bold{\purple{S.I =\: Rs\: 876}}$

Again, we have to find the compound interest :

As we know that :

$\bigstar$ Amount Formula :

$\mapsto \sf\boxed{\bold{\pink{A =\: P\bigg[1 + \dfrac{r}{100}\bigg]^{n}}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time Period

Given :

• Principal = Rs 7300
• Rate of Interest = 6% p.a.
• Time Period = 2 years

According to the question by using the formula we get,

$\implies \sf A =\: 7300\bigg[1 + \dfrac{6}{100}\bigg]^{2}$

$\implies \sf A =\: 7300\bigg[\dfrac{106}{100}\bigg]^2$

$\implies \sf A =\: 7300 \times \dfrac{106}{100} \times \dfrac{106}{100}$

$\implies \sf A =\: \dfrac{\cancel{82022800}}{\cancel{10000}}$

$\implies \sf\bold{\green{A =\: Rs\: 8202.28}}$

Now, we have to find compound interest :

As we know that :

$\bigstar$ Compound Interest or C.I Formula :

$\mapsto \sf\boxed{\bold{\pink{C.I =\: A - P}}}$

where,

• C.I = Compound Interest
• A = Amount
• P = Principal

Given :

• Amount = Rs 8202.28
• Principal = Rs 7300

According to the question by using the formula we get,

$\leadsto \sf C.I =\: Rs\: 8202.28 - Rs\: 7300$

$\leadsto \sf\bold{\purple{C.I =\: Rs\: 902.28}}$

Now, we have to find the difference between simple interest and compound interest :

Given :

• Compound Interest = Rs 902.28
• Simple Interest = Rs 876

According to the question by using the formula we get,

$\longrightarrow \footnotesize \sf\bold{\pink{Difference\: Between =\: C.I - S.I}}$

$\longrightarrow \footnotesize \sf Difference\: Between =\: Rs\: 902.28 - Rs\: 876$

$\longrightarrow \footnotesize \sf\bold{\red{Difference\: Between =\: Rs\: 26.28}}$

$\therefore$ The difference between the simple interest and compound interest is Rs 26.28.

Answer 2

Answer:

${\large{\underline{\underline{\textsf{\textbf{Given\:: -}}}}}}$

• ➯ Principle = Rs.7300
• ➯ Rate of Interest = 6% per annum
• ➯ Time = 2 years

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

${\large{\underline{\underline{\textsf{\textbf{To Find\:: -}}}}}}$

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

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

${\large{\underline{\underline{\textsf{\textbf{Using Formulae\:: -}}}}}}$

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

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

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

$\bigstar{\underline{\boxed{\bf{\red{Difference = C.I - S.I}}}}}$

$\pink\bigstar$ Where

• ➯ S.I = Simple Interest
• ➯ P = Principle
• ➯ T = Time
• ➯ R = Rate
• ➯ A = Amount
• ➯ C.I = Compound Interest

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

${\large{\underline{\underline{\textsf{\textbf{Solution\:: -}}}}}}$

$\pink\bigstar$ Finding Simple Interest

${\dashrightarrow{\sf{Simple \: Interest = \dfrac{P \times R \times T}{100}}}}$

• Substuting the values

${\dashrightarrow{\sf{Simple \: Interest = \dfrac{7300\times 6\times 2}{100}}}}$

${\dashrightarrow{\sf{Simple \: Interest = \dfrac{7300\times 12}{100}}}}$

${\dashrightarrow{\sf{Simple \: Interest = \dfrac{87600}{100}}}}$

${\dashrightarrow{\sf{Simple \: Interest = \cancel{\dfrac{87600}{100}}}}}$

${\dashrightarrow{\sf{Simple \: Interest = Rs.876}}}$

$\bigstar{\underline{\boxed{\bf{\green{Simple \: Interest = Rs.876}}}}}$

∴ The simple interest is Rs.876.

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

$\pink\bigstar$ Finding Amount

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

• Substuting the values

${\dashrightarrow{\sf{Amount=7300{\bigg(1 + \dfrac{6}{100}{\bigg)}^{2}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg(\dfrac{100 + 6}{100}{\bigg)}^{2}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg(\dfrac{106}{100}{\bigg)}^{2}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg( \cancel{\dfrac{106}{100}}{\bigg)}^{2}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg(\dfrac{53}{50}{\bigg)}^{2}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg(\dfrac{53}{50} \times \dfrac{53}{50}{\bigg)}}}}}$

${\dashrightarrow{\sf{Amount=7300{\bigg( \dfrac{2809}{2500}{\bigg)}}}}}$

${\dashrightarrow{\sf{Amount=7300 \times \dfrac{2809}{2500}}}}$

${\dashrightarrow{\sf{Amount= \dfrac{7300 \times 2809}{2500}}}}$

${\dashrightarrow{\sf{Amount= \dfrac{20505700}{2500}}}}$

${\dashrightarrow{\sf{Amount= \cancel{\dfrac{20505700}{2500}}}}}$

${\dashrightarrow{\sf{Amount= Rs.8202.28}}}$

$\bigstar{\underline{\boxed{\bf{\green{Amount= Rs.8202.28}}}}}$

∴ The Amount is Rs.8202.28.

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

$\pink\bigstar$ Now, Calculating the compound interest

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

• Substuting the values

${\dashrightarrow{\sf{Compound \: Interest= 8202.38 - 7300}}}$

${\dashrightarrow{\sf{Compound \: Interest= Rs.902.28}}}$

$\bigstar{\underline{\boxed{\bf{\green{Compound \: Interest= Rs.902.28}}}}}$

∴ The compound interest is Rs.908.28.

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

$\pink\bigstar$ Now, Finding the difference between simple interest and compound interest

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

• Substuting the values

${\dashrightarrow{\sf{Difference = 902.28 - 876}}}$

${\dashrightarrow{\sf{Difference = Rs.26.28}}}$

$\bigstar{\underline{\boxed{\bf{\green{Difference = Rs.26.28}}}}}$

∴ The difference between simple interest and compound interest is Rs.26.28.

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

${\large{\underline{\underline{\textsf{\textbf{Answer\: : -}}}}}}$

➤ The Difference between simple interest and compound interest on ₹7300 at the rate of 6% per annum in 2 years is Rs.26.28.

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

${\large{\underline{\underline{\textsf{\textbf{Learn More\: : -}}}}}}$

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

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

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

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

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

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

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

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