Question

calculate the compound intrest on ₹ 10,000 for 2 years at 7% p.a.​

Answer 1

Given :

• Principal = ₹ 10,000
• Time = 2 years
• Rate = 7%

To find :

• Compound Interest

Knowledge required :-

→ Formula to calculate amount :-

$\star \qquad\underline{\boxed{ \bf{ \blue{Amount = P \Bigg[1 + \dfrac{r}{100} \Bigg] ^n}}}}$

$\bf{where,}$

• P = Principal
• r = rate
• n = time

→ Formula to calculate Compound Interest, when Principal and Amount is given.

$\star \qquad \underline{ \boxed{ \bf \blue{Compound \: \: Interest = Amount - Principal }}}$

Solution :

$\\ : \implies\sf{Amount = P \Bigg[1 + \dfrac{r}{100} \Bigg] ^n}$

$\\ : \implies\sf{Amount = 10000 \Bigg[1 + \dfrac{7}{100} \Bigg] ^2}$

$\\ : \implies\sf{Amount = 10000 \Bigg[ \dfrac{100 + 7}{100} \Bigg] ^2}$

$\\ : \implies\sf{Amount = 10000 \Bigg[ \dfrac{107}{100} \Bigg] ^2}$

$\\ : \implies\sf{Amount = 10000 \times \dfrac{107}{100} \times \dfrac{107}{100}}$

$\\ : \implies\sf{Amount = 1 \not0 \not0 \not0 \not0 \times \dfrac{107}{1 \not0 \not0} \times \dfrac{107}{1 \not0 \not0}}$

$\\ : \implies\sf{Amount = 107 \times 107}$

$\\ : \implies\bf{Amount = 11449}$

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

$\\ :\implies \sf{Compound \: \: Interest = 11449 - 10000 }$

$\\ :\implies \bf{Compound \: \: Interest = Rs. \: 1449 }$

$\red \bigstar \quad \underline{\pmb {Compound \: \: Interest = Rs. \: 1449} }$

Answer 2

Given :-

• Principal (P) = Rs 10000
• Time (n) = 2 years
• Rate (R) = 7% per annum

To Find :-

• Compound interest

Formulas :-

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

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

Solution :-

${:} \longrightarrow \sf \: Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000 \: \times \bigg(\:1 \: + \: \dfrac{7}{100}\bigg)^{2} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000 \: \times \bigg(\dfrac{107}{100}\bigg)^{2} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000\: \times \: \dfrac{107}{100} \: \times \: \dfrac{107}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 1\cancel{0000} \: \times \: \dfrac{107}{1 \cancel{00}} \: \times \: \dfrac{107}{1 \cancel{00}} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 107 \: \times \: 107\\ \\ {:} \longrightarrow \underline{\boxed{\sf \: Amount \: = \: Rs \: 11449}} \: \blue \bigstar$

━━━━━━━━━━

$\longmapsto {\pmb{ Compound \: Interest \: = \: Amount \: - \: Principal} } \\ \\ \longmapsto {\sf{ Compound \: Interest \: = \: 11449 \: - \: 10000} } \\ \\ \longmapsto \underline{\boxed{\pmb{ \red{ Compound \: Interest \: = \:Rs \:1449} }}}$

━━━━━━━━━━

$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs \: 11499}}}$

$\qquad \therefore\: \sf{ Compound \: Interest\: = \underline {\underline{ Rs \: 1449}}}$

━━━━━━━━━━