Question

calculate the amount and compound interest on rs.10800 for 3 years at 25/2% per annum​

Answer 1

Answer :

• Amount = ₹15377.34
• Compound interest = ₹4577.34

Explanation :

Principal ₹10,800 is to compounded for 3 years at the rate of 25/2% p. a. (per annum)

Calculate the amount and the C. I. (compound interest).

We know that,

→ C. I. = Amount - principal

Using amount formula,

• Amount = p(1 + r/100)ⁿ

Where,

• p(principal) = ₹10,800
• r(rate) = 25/2% p.a.
• n(time) = 3 years.

So, the amount is -

→ 10,800(1 + 25/100*2)³

→ 10,800(1 + 25/200)³

→ 10,800(1 + 1/8)³

→ 10,800(9/8)³

→ 10,800 × 729/512

→ 15377.34

∴ Amount = ₹15377.34

Hence, the C. I. will be -

→ 15377.34 - 10,800

→ 4577.34

Answer 2

Given :

• Principal (P) = Rs 10800
• Time (n) = 3 years
• Rate (R) = 25/2% 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 :

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

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \bigg(1 \: + \: \dfrac{25}{100}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \bigg(1 \: + \: \dfrac{ \dfrac{25}{2} }{100}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \bigg(1 \: + \: \dfrac{25}{100 \: \times \: 2}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \bigg(1 \: + \: \dfrac{25}{200}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \bigg(1 \: + \: \dfrac{1}{8}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \bigg( \dfrac{9}{8}\bigg)^{3}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \dfrac{9}{8} \: \times \: \dfrac{9}{8} \: \times \: \dfrac{9}{8}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \dfrac{9 \: \times \: 9 \: \times 9}{8 \: \times \: 8 \: \times \: 8}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: \dfrac{729}{512}$

${:} \longrightarrow \sf \: Amount \: = \: 10800 \: \times \: 1.42$

${:} \longrightarrow \underline {\boxed { \color{lime} \bf \: Amount \: = \: Rs \: 15336 \qquad \: \red{(approx)} }} \color{navy} \: \: \bigstar$

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

${:} \longrightarrow \sf \: Compound \: Interest \: = \: 15336 \: - \: 10800$

${:} \longrightarrow \underline {\boxed { \color{aqua} \bf \: Compound \: Interest \: = \: Rs \: 4536 }} \color{pink} \: \: \bigstar$

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$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs \: 15336}}}$

$\qquad \therefore\: \sf{ Compound \: Interest \: = \underline {\underline{ Rs \: 4336}}}$

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