Question

P=1200 T=2 R=20 find the compound internet

Answer 1

★ Solution :-

First, we should find the amount that will obtain with these values. We have a formula for finding that,

Amount :-

$\sf \leadsto Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \leadsto 1200 \bigg( 1 + \dfrac{20}{100} \bigg)^{2}$

$\sf \leadsto 1200 \bigg( 1 + \dfrac{1}{5} \bigg)^{2}$

$\sf \leadsto 1200 \bigg( \dfrac{5 + 1}{5} \bigg)^{2}$

$\sf \leadsto 1200 \bigg( \dfrac{6}{5} \bigg)^{2}$

$\sf \leadsto 1200 \bigg( \dfrac{6^2}{5^2} \bigg)$

$\sf \leadsto 1200 \bigg( \dfrac{36}{25} \bigg)$

$\sf \leadsto \dfrac{1200 \times 36}{25} = \dfrac{443200}{25}$

$\sf \leadsto \cancel \dfrac{443200}{25} = 1728$

Now, we can find the compound interest.

Compound interest :-

$\sf \leadsto CI = Amount - Principle$

$\sf \leadsto 1728 - 1200$

$\sf \leadsto Rs.528$

Therefore, the compound interest is ₹528.

Answer 2

Given :

Principal (P) = 1200

Time (T) = 2 years

Rate (R) = 20%

What To Find :

We have to find C.I.

• C.I. = Compound Interest

Formula Using :

$\large\begin{gathered} {\underline{\boxed{ \rm {\red{A \: = \: P \:\bigg( \: 1 \: + \: \frac{r}{100} \bigg)^{t} }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {\blue{C.I = A - P}}}}}\end{gathered}$

Where ,

• A denotes Amount
• P denotes Principal
• R denotes Rate of interest
• t denotes time (in years).
• C.I. denotes Compound Interest

Basic Terms :

• Simple Interest = Simple interest is the method of calculating interest charged on the amount invested in a fixed deposit.

• Principle = The principal is the amount due on any debt before interest, or the amount invested before returns.

• Rate = An interest rate is the percentage of principal charged by the lender for the use of its money.

• Time = Time is duration (in months or years) in Simple Interest.

Solution :

For finding compound Interest first we need to find amount , after then we find compound Interest .

Here ,

$\bf\green{ \longmapsto} \rm \:Principal \: = \: 1200$

$\bf\green{ \longmapsto} \rm \:Rate \: of \: interest \: = \: 20 \: \%$

$\bf\green{ \longmapsto} \rm \:Time \: = \: 2 \: years$

$\red \maltese \: \large{\textrm{{{\color{navy}{Calculating the Compound Interest}}}}}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: P \: \bigg( \: 1 \: + \: \frac{r}{100} \bigg) ^{t}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \bigg( \: 1 \: + \: \frac{20}{100} \bigg) ^{2}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \bigg( \: 1 \: + \: \frac{ \cancel{20}}{ \cancel{100}} \bigg) ^{2}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \bigg( \: 1 \: + \: \frac{ {1}}{{5}} \bigg) ^{2}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \bigg( \frac{5 \: + \: 1}{5} \bigg) ^{2}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \bigg( \frac{6}{5}\bigg) ^{2}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 1200 \: \times \: \frac{6}{5} \: \times \: \frac{6}{5}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: \cancel {1200} \: \: ^{240} \: \times \: \frac{6}{5} \: \times \: \frac{6}{ \cancel5}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: \cancel{240} \: \: ^{48} \: \times \: \frac{6}{ \cancel5} \: \times \: {6}$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = \: 48 \: \times \: 6 \: \times \: 6$

$\large\bf\purple{ \longrightarrow} \rm \:A \: = 1728$

$\Large\underbrace{\mathcal {{{\color{orange}{ \: Amount = 1728 \: }}}}}$

$\large \blue\dag \: \underline {\rm {{{\color{green}{For \: , \: Finding \: C.I.}}}}} \: \blue \dag$

$\large\bf\purple{ \hookrightarrow} \rm \:C.I = Amount \: - \: Principal$

$\large\bf\purple{ \hookrightarrow} \rm \:C.I = \: 1728 \: - \: 1200$

$\large\bf\purple{ \hookrightarrow} \rm \:C.I = \: ₹ \: 528$

$\Large\underbrace{\mathcal {{{\color{blue}{ \: Compound \: Interest \: = \: ₹ \: 528 }}}}}$