Question

find the amount and compound interest on $8000 at 5% per annum for 2 years compound annually​

Answer 1

Given :

• Principal = 8000

• Rate = 5%

• Time = 2 years

To Find :

• Amount and compound interest

Solution :

✬ As in the question principal, rate of intrerst and time is given.So by using the amount formula that is P (1 + R/100)ⁿ we will find the amount and after finding the amount Using the formula of compound interest That is Amount - Principal. we can find the required Compound interest

Amount = P (1 + R/100)ⁿ

Where,

• ⇝Principal (P) = Rs.8000

• ⇝ Time (n) = 2 years

• ⇝ Rate (R) = 5%

⟶ Amount = 8000 ( 1 + 5/100)²

⟶ Amount = 8000 × (105/100)²

⟶ Amount = 8000 × 105/100 × 105/100

⟶ Amount = 4 × 105 × 21

⟶ Amount = Rs 8820

____________________

Now, Compound interest

C.I = Amount - Principal

⟶ C.I = 8820 - 8000

⟶ C.I = Rs. 820

____________________

∴ Compound interest is Rs. 820

Answer 2

Given :

• Principal (P) = Rs 8000
• Time (n) = 2 years
• Rate (R) = 5% per annum

To Find :

• Amount
• Compound Interest

Formula :

$\red \bigstar \: {\underline \orange {\boxed{\mathcal {\pmb{\color{aqua}\quad Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n} \quad}}}}}$

$\red \bigstar \: {\underline \orange {\boxed{\mathcal {\pmb{\color{aqua}\quad Compound \: Interest \: = \: Amount \: - \: Principal \quad}}}}}$

Solution :

${:} \longrightarrow \sf \: Amount \: = \: Principal \: \times \bigg(1 \: + \: \dfrac{Rate}{100}\bigg)^{n}$

${:} \longrightarrow \sf \: Amount \: = \: 8000 \: \times \bigg(1 \: + \: \dfrac{5}{100}\bigg)^{2}$

${:} \longrightarrow \sf \: Amount \: = \: 8000 \: \times \: \bigg(1 \: + \: \dfrac{ 1}{20}\bigg)^{2}$

${:} \longrightarrow \sf \: Amount \: = \: 8000 \: \times \: \bigg(\dfrac{21}{20}\bigg)^{2}$

${:} \longrightarrow \sf \: Amount \: = \: 8000 \: \times \: \dfrac{21}{20} \: \times \: \dfrac{21}{20}$

${:} \longrightarrow \sf \: Amount \: = \: \dfrac{80 \: \times \: 21 \: \times \: 21}{2 \: \times \: 2}$

${:} \longrightarrow \sf \: Amount \: = \: \dfrac{80 \: \times \: 441}{4}$

${:} \longrightarrow \sf \: Amount \: = \: \dfrac{35280}{4}$

${:} \longrightarrow \underline {\boxed { \color{lime} \bf \: Amount \: = \: Rs \: 8820 }} \color{navy} \: \: \bigstar$

___________________

${:} \longrightarrow \sf \: Compound \: Interest \: = \: Amount \: - \: Principal$

${:} \longrightarrow \sf \: Compound \: Interest \: = \: 8820 \: - \: 8000$

${:} \longrightarrow \underline {\boxed { \color{aqua} \bf \: Compound \: Interest \: = \: Rs \: 820 }} \color{pink} \: \: \bigstar$

___________________

$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs \: 8820}}}$

$\qquad \therefore\: \sf{ Compound \: Interest \: = \underline {\underline{ Rs \: 820}}}$

___________________