Question

find the compound interest when it is compound annually when principal 3200Rs, r 25% per annum and time 3 year.​

Answer 1

Step-by-step explanation:

Given:-

• Principal (P) = Rs.3200

• Rate (r) = 25%

• Time (n) = 3 years

To Find:-

• Compound Interest compounded annually.

Solution:-

For calculating Compound Interest first we need to find Amount

As we know that:-

The formula for calculating Amount is:-

$\boxed{\sf Amount = P\bigg(1 + \dfrac{r}{100}\bigg)^{n}}$

$\implies \sf A = 3200 \times \bigg(1 + \dfrac{25}{100}\bigg)^{3}$

$\implies \sf A = 3200 \times \bigg( \dfrac{125}{100}\bigg)^{3}$

$\implies \sf A = 3200 \times \bigg( \dfrac{5}{4}\bigg)^{3}$

$\implies \sf A = 3200 \times \dfrac{5 \times 5 \times 5}{4 \times 4 \times 4}$

$\implies \sf A = 3200 \times \dfrac{125}{64}$

$\implies \sf A = 50 \times 125$

$\implies \sf A = 6250$

$\therefore \underline{\:\: \underline{\: \sf Amount = Rs.6250\:}\:\:}$

$\sf Compound \: Interest = Amount - Principal$

$\sf = 6250 - 3200$

$\sf = 3050$

$\large\underline{ \boxed{ \therefore\textsf{ \textbf{Compound \: Interest = Rs.3050}}}}$

Answer 2

Answer:

Given :-

• $\purple\mapsto$$\sf\red{Principal - Rs.3200}$
• $\purple\mapsto$$\sf\red{Rate - 25\:percent}$
• $\purple\mapsto$$\sf\red{Time - 3 years }$

To Find -

• ${\orange\rightarrow\sf\blue{Compound\:Interest\:compound\: annually} }$

Using Formula -

$\pink{⟹}$$\sf \small \pink{Amount }= \purple{P(1 + {\dfrac{r}{100}})^{t}}$

$\pink{⟹}$$\sf \small\orange{Compound \: Interest = \green{Amount-Principal}}$

Solution -

Firstly we Find the Amount :-

$\red\leadsto$$\sf \small \pink{A }= \purple{3200(1 + {\dfrac{25}{100}})^{3}}$

$\red\leadsto$$\sf \small \pink{A }= \purple{3200×( {\dfrac{100 + 25}{100}})^{3}}$

$\red\leadsto$$\sf \small \pink{ A}= \purple{3200 \times ({\dfrac {\cancel{125}}{ \cancel{100}}})^{3}}$

$\red\leadsto$$\sf \small \pink{A}= \purple{3200 \times ({\dfrac{5}{4}})^{3}}$

$\red\leadsto$$\sf \small \pink{A}= \purple{3200 \times ({\dfrac{5 \times 5 \times 5}{4 \times 4 \times 4}})}$

$\red\leadsto$$\sf \small \pink{A}= \purple {\cancel{3200} \times ( {\dfrac{125} {\cancel{64}}})^{}}$

$\red\leadsto$$\sf \small \pink{A }= \purple{(50 \times 125 )}$

$\red\leadsto$$\sf \small \pink{A} = \purple {6250}$

$\large \boxed{\sf{ \pink{Amount} ={\purple{6250}}}}$

Now we Find the Compount Interest :-

$\purple\leadsto$$\sf \small\orange{Compound \: Interest = \green{6250 - 3200}}$

$\purple\leadsto$$\sf\small\orange{Compound\:Interest={\green{3050}}}$

Therefore :-

$\large\boxed{\sf{\orange{{Compound\:Interest=}}Rs.{\green{3050}}}}$