Question

₹6400 for 2 years at 15% p.a. compounded annually.

Answer 1

Given :

• ➙ Principal = 6400
• ➙ Rate = 15 %
• ➙ Time = 2 years

$\rule{200pt}{3pt}$

To Find :

• ➙ Compound Interest = ?
• ➙ Amount = ?

$\rule{200pt}{3pt}$

Solution :

✴ Formula Used :

$\large{\color{blue}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ C.I = P \bigg\lgroup1 + \dfrac{R}{100} \bigg\rgroup^T - P }}}}}$

$\\ \large{\color{blue}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Amount = P + C.I }}}}}$

Where :

• ➳ C.I = Compound Interest
• ➳ P = Principal
• ➳ R = Rate
• ➳ T = Time

${\qquad{\rule{150pt}{1pt}}}$

✴ Calculating the Compound Intrest :

${\dashrightarrow{\qquad{\sf{ C.I = P \bigg\lgroup1 + \dfrac{R}{100} \bigg\rgroup^T - P }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 6400 \bigg\lgroup1 + \dfrac{15}{100} \bigg\rgroup^2 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 6400 \bigg\lgroup1 + \cancel\dfrac{15}{100} \bigg\rgroup^2 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 6400 \bigg\lgroup1 + 0.15 \bigg\rgroup^2 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{C.I = 6400 \bigg\lgroup1.15 \bigg\rgroup^2 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 6400 \times 1.15 \times 1.15 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 6400 \times 1.3225 - 6400 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{C.I = 8464 - 6400 }}}} \\ \\ \ \large{\qquad{\orange{:\longmapsto{\underline{\overline{\boxed{\purple{\sf{ ₹ \: 2064 }}}}}}}}}{\pink{\bigstar}}$

$\qquad{\rule{150pt}{1pt}}$

✴ Calculating the Amount :

${\dashrightarrow{\qquad{\sf{ Amount = P + C.I }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Amount = 6400 + 2064 }}}} \\ \\ \ \large{\qquad{\orange{:\longmapsto{\underline{\overline{\boxed{\color{green}{\sf{ ₹ \: 8464 }}}}}}}}}{\pink{\bigstar}}$

$\qquad{\rule{150pt}{1pt}}$

✴ Therefore :

❝ Compound Interest on this sum of money is ₹ 2064 and the Amount is ₹ 8464 . ❞

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

Answer:

Right Question :

Find the compound interest on Rs. 6400 for 2 years, compounded annually at 15% per annum.

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

Given :

• ➞ Principle = Rs.6400
• ➞ Time = 2 years
• ➞ Rate = 15% per annum.

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

To Find :

• ➞ Amount
• ➞ Compound Interest

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

Concept :

➭ Here we have given that the Principal is Rs.6400, Time is 2 years and Rate is 15 p.c.p.a. 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.

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

Using Formulas :

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

$\longrightarrow\small{\underline{\boxed{\sf{{C.I=A- P}}}}}$

Where :

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

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

Solution :

Firstly, finding the amount by substituting the values in the formula :

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

$\dashrightarrow \: \: {\sf{A= 6400\bigg(1 + \dfrac{15}{100} \bigg)^{2}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg(\dfrac{(1 \times 100) + (15 \times 1)}{100} \bigg)^{2}}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg(\dfrac{100 + 15}{100} \bigg)^{2}}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg(\dfrac{115}{100} \bigg)^{2}}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg(\cancel{\dfrac{115}{100}} \bigg)^{2}}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg( \dfrac{23}{20} \bigg)^{2}}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg( \dfrac{23}{20} \times \dfrac{23}{20} \bigg)}}}$

${\dashrightarrow \: \: {\sf{A= 6400\bigg( \dfrac{529}{400} \bigg)}}}$

${\dashrightarrow \: \: {\sf{A= 6400 \times \dfrac{529}{400}}}}$

${\dashrightarrow \: \: {\sf{A= \cancel{6400}\times \dfrac{529}{\cancel{400}}}}}$

${\dashrightarrow \: \: {\sf{A= 16 \times 529}}}$

${\dashrightarrow \: \: {\sf{A= Rs.8464}}}$

${\bigstar \: \pink{\underline{\boxed{\sf{Amount= Rs.8464}}}}}$

∴ The amonut is Rs.8464.

$\rule{300}{1.5}$

Now, finding the compound interest by substituting the values in the formula :

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

$\dashrightarrow \: \: {\sf{{C.I=8464 - 6400}}}$

$\dashrightarrow \: \: {\sf{{C.I=Rs.2064}}}$

${\bigstar \: \pink{\underline{\boxed{\sf{Compund \: Interest= Rs.2064}}}}}$

∴ The compound interest is Rs.2064.

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

Learn More :

»» Principal: Money which is taken or given in the form of loan. That's called the principal. It is denoted by P.

»» Time: The period for which the loan is taken or given is called time. It is expressed by T or t.

»» Rate: The rate at which interest is charged or paid is called interest rate. It is denoted by r or R.

»» Interest: In addition to the principal amount, which is refunded, interest is paid. It is denoted by I.

»» Amount: For example, money taken is called principal and money returned is called compound.

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

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

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

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

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

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

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

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

${\rule{220pt}{2.5pt}}$