Question

If principle (P)= ₹5000 Rate (R) =8p.c.p.a. Duration (N)= 3years Amount (A)= ? , Compound interest= ?

₹6298.56,₹1298.56
₹5803.63,₹2198.56
₹6982.65,₹1982.57
₹6842.98,₹2198.63​

Answer 1

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Given:}}}}}$

✰ Principle ( P ) = ₹5000

✰ Rate ( r ) = 8%

✰ Time ( n ) = 3 years

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{To \: Find:}}}}}$

✠ Amount ( A )

✠ Compound interest ( C.I. )

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Solution:}}}}}$

ㅤㅤㅤㅤㅤ

When interest is compounded yearly the formula for finding amount is:

${\bigstar{ \large {\boxed {\green {\sf{A = P{ {\bigg(1} + \dfrac{r}{100}{\bigg)}^{n} } }}}}}}$

ㅤㅤㅤㅤㅤ

where

A = amount;

P = principal

r = rate of interest compounded

n = number of years

$\\ \\ \implies \sf{A = 5000{ {\bigg(1} + \dfrac{8}{100}{\bigg)}^{3} } }$

$\\ \\ \implies \sf{A = 5000 {{ \bigg(} \dfrac{100 + 8}{100}{\bigg)}^{3} } }$

$\\ \\ \implies \sf{A = 5000 {{ \bigg(} \dfrac{108}{100}{\bigg)}^{3} } }$

$\\ \\ \implies \sf{A = 5000 {{ \bigg(} \dfrac{54}{50} {\bigg)}^{3} } }$

$\\ \\ \implies \sf{A = 5000 \times {{ \bigg(} \dfrac{27}{25} {\bigg)}^{3} } }$

$\\ \\ \implies \sf{A = 5000 \times \dfrac{27}{25} \times \dfrac{27}{25} \times \dfrac{27}{25} }$

$\\ \\ {\blue { \implies \sf{A = 6298.56}}}$

ㅤㅤㅤㅤㅤ

∴ Amount = ${ \green{\boxed {\sf{ \gray{ Rs. \: 6298.56}}}}}$

ㅤㅤㅤㅤㅤ

ㅤㅤㅤㅤㅤ

Now, let's find out compound interest ( C.I. )

${\bigstar{ \large {\boxed {\green {\sf{C.I. = A - P}}}}}}$

$\\ \implies{ \sf{C.I. = 6298.56 - 5000}}$

$\\ {\blue {\implies{ \sf{C.I. = 1298.56}}}}$

ㅤㅤㅤㅤㅤ

∴ Compound interest (C.I.) = ${\green{\boxed {\sf{ \gray{ Rs \: 1298.56}}}}}$

ㅤㅤㅤㅤㅤ

▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬

Answer 2

Given :-

• Principal (P) = Rs,5000
• Rate (R) = 8%
• Time (n) = 3years

To Find :-

• Amount and Compound Interest

Formulas :-

$\red \bigstar \: \:{ \large \underline{\boxed {\sf{Amount \: = \: Principal \: { {\bigg(1} + \dfrac{rate}{100}{\bigg)}^{n} } }}}} \: \: \red \bigstar \\ \\ \blue \bigstar \: \:{ \large \underline{\boxed {\sf{Compound \: interest\: = \: Amount \: - \: Principal}}}}\: \: \blue \bigstar$

Solution :-

${:} \longrightarrow \: \: {\sf{Amount \: = \: Principal \: { {\bigg(1} + \dfrac{rate}{100}{\bigg)}^{n} } }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: = \: 5000 \: { {\bigg(1} + \dfrac{8}{100}{\bigg)}^{3} } }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: = \: 5000 \: { {\bigg(} \dfrac{108}{100}{\bigg)}^{3} } }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: = \: 5 \cancel{000} \: \times \: \dfrac{108}{1 \cancel{00}} \: \times \: \dfrac{108}{10 \cancel0} \: \times \: \dfrac{108}{100}}} \\ \\{:} \longrightarrow \: \: {\sf{Amount \: = \: \cancel5 \: \times \: \dfrac{108 \: \times \: 108 \: \times \: 108}{ \cancel{1000}} }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: =\: \dfrac{108 \: \times \: 108 \: \times \: 108}{ 200} }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: =\: \dfrac{11664 \: \times \: 108}{ 200} }} \\ \\ {:} \longrightarrow \: \: {\sf{Amount \: =\: \dfrac{ 1,259,712}{ 200} }} \\ \\ {:} \longrightarrow \: \: {\sf \boxed{ \bf{Amount \: =\:Rs, 6298.56}}} \: \green \bigstar$

________________

$\longmapsto \: \: {\sf{Compound \: interest\: = \: Amount \: - \: Principal}} \\ \\ \longmapsto \: \: {\sf{Compound \: interest\: = \: 6298.56 \: - \: 5000}} \\ \\ \longmapsto \: \: {\sf \boxed{ \bf{Compound \: interest\: = \: Rs,1298.56}}} \: \: \green \bigstar$

________________

$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs,6298.56}}}$

$\qquad \therefore\: \sf{ Compound\: Interest \: = \underline {\underline{ Rs,1298.56}}}$

________________