Question

calculate the amount and the compound intrest on$12000 in 2 years in 8 %per annum compounded anually​

Answer 1

$\large{\underline{\boxed{ \boxed{\sf Let's \: Understand \: Concept \: F1^{st}}}}}$

Here, we have given the principal which is compounded annually at the rate of 8% per annum for 2years. and have to find the amount and Compund Interest on it. After using Formula for Amount we will substitute given values in it and got the amount. Then, for the Compund Interest we will subtract Principal from Amount.

$\huge{\underline{\boxed{\sf Answer}}}$

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$\large{\underline{\sf Given:-}}$

❑Principal = $12000

❑Rate = 8%

❑Time = 2yrs

$\large{\underline{\sf Find:-}}$

❑Amount

❑Compound Interest

$\large{\underline{\sf Solution:-}}$

we, know that

$\underline{\boxed{\sf Amount =P { \bigg\lgroup{\sf 1+\dfrac{R}{100}} \bigg\rgroup}^n}}$

where,

• Principal, P = $12000
• Rate, R = 8%
• Time, n = 2yrs

So,

$\dashrightarrow\sf Amount =P { \bigg\lgroup{\sf 1+\dfrac{R}{100}} \bigg\rgroup}^n$

$\dashrightarrow\sf Amount =12000 { \bigg\lgroup{\sf 1+\dfrac{8}{100}} \bigg\rgroup}^2$

$\sf \bigstar Taking \: L.C.M \bigstar$

$\dashrightarrow\sf Amount =12000 { \bigg\lgroup{\sf \dfrac{100 + 8}{100}} \bigg\rgroup}^2$

$\dashrightarrow\sf Amount =12000 { \bigg\lgroup{\sf \dfrac{108}{100}} \bigg\rgroup}^2$

$\dashrightarrow\sf Amount =12000 \times \dfrac{108}{100} \times \dfrac{108}{100}$

$\dashrightarrow\sf Amount =12000 \times \dfrac{11664}{10000}$

$\dashrightarrow\sf Amount =\dfrac{139968000}{10000}$

$\dashrightarrow\sf Amount = \ 13996.8$

$\small{\therefore \underline{\sf Amount = \ 13996.8}}$

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⇰Compund Interest, C.I. = Amount - Principal

where,

• Amount, A = $13996.8
• Principal, P = $12000

So,

➮Compound Interest = 13996.8 - 12000

➮Compound Interest = $1996.8

∴Compund Interest = $1996.8

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Hence,

• Amount, A = $13996.8
• Compound Interest, C.I. = $1996.8

Answer 2

$\huge \red \star \: \: \huge \sf \underline{ \blue{given : }} \: \: \huge \red \star \:$

• P = 12000$
• n = 2years
• T = 8% per annum

$\huge \red \star \: \: \huge \sf \underline{ \blue{to \: find : }} \: \: \huge \red \star$

• Amount(A).
• Compound intreast (C.I)

$\huge \red \star \: \: \huge \sf \underline{ \blue{answer : }} \: \: \huge \red \star \:$

$\boxed{ \tt{amount = </p><p>P \: ( { 1 + \frac{</p><p>R}{100} ) }^{n} }} \:$

Putting values in formula , we get,

$\to \tt{12000 \: ( {1 + \frac{8}{100} )}^{2} } \\ \\ \to \tt{12000( { \frac{100 + 8}{100} )}^{2} } \\ \\ \to \tt{12000 \:( { \frac{108}{100}) }^{2} } \\ \\ \to\tt{12000( \frac{11664}{10000}) } \\ \\ \to \tt{ \: 13996.8}$

Amount (A) = 13996.8 $

$\boxed{ \tt{c.i = A - P}} \:$

C.I = 13996.8 - 12000

C.I = 1996.8 $

∴ Amount is 13996.6 $ and C.I is 1996.8 $ .