Question

*What is the amount for Rs. 10000 by compound interest at 8% rate for 2 years?*

1️⃣ ₹ 5000
2️⃣ ₹ 11664
3️⃣ ₹ 15664
4️⃣ ₹ 10664​

Answer 1

Given : ↴

$\sf \: Principal \: : \: Rs. \: 10000$

$\sf \: Rate \: of \: Interest \: : \: 8 \: \%$

$\sf \: Time \: : \: 2 \: years$

To find : ↴

$\sf \: We \: have \: to \: find \: the \: Amount.$

So, let's do it : ↴

$\sf \: Formula \: to \: find \: the \: Amount \: is :$ ↴

$\boxed { \sf \: Amount \: = \: Principal \bigg(1 \: + \: \dfrac{Rate \: of \: Interest}{100} \bigg )^{Time} } \: \:$

$\sf \longrightarrow \: Amount \: = \: 10000\bigg(1 \: + \: \dfrac{8}{100} \bigg )^{2} \: \:$

$\sf \: First \: of \: all \: cancel \: the \: common \: factor \: of \: 8 \: and \: 100.$

$\sf \longrightarrow \: 10000\bigg(1 \: + \: \dfrac{2}{25} \bigg )^{2} \: \:$

$\sf \: Now \: Simplify \: the \: expression.$

$\sf \longrightarrow \: 10000\bigg( \dfrac{25 \: + \: 2}{25} \bigg )^{2} \: \:$

$\sf \: Now \: add \: 25 \: and \: 2.$

$\sf \longrightarrow \: 10000\bigg( \dfrac{27}{25} \bigg )^{2} \: \:$

$\sf \: Again \: Simplify \: the \: expression.$

$\sf \longrightarrow \: 10000 \: \times \: \bigg(\dfrac{729}{625} \bigg)$

$\sf \: Here, \: cancel \: the \: common \: factor \: of \: 625.$

$\sf \longrightarrow \: 16 \: \times \: 729$

$\sf \longrightarrow \: Multiply \: 16 \: by \: 729.$

$\sf \longrightarrow \: 11664 \: is \: the \: Answer..$

$\boxed { \sf \longrightarrow \: Amount \: = \: 11664}$

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$\sf More \:that\: can \:be\: Solved\: :$ ↴

$\boxed { \sf \:Comound \: Interest \: = \:Amount \: - \: Principal}$

$\sf \:Comound \: Interest \: = \: 11664\: - \: 10000$

$\boxed { \sf \:Comound \: Interest \: = \: Rs. \: 1664}$

Answer 2

Answer:

Given

Principal=10000

Rate=8%

Time/n=2 years

To find

Amount

$\bold\blue{By \ using \ formula \</p><p></p><p> Amount=P(1 \ + \ R/100)^n}$

Solution

Amount=$\bold\pink{Amount=P(1 \ + \ R/100)^n}$

∴$\bold\purple{10000(1 \ + \ 8/100)^2}$

∴$\bold\orange{10000(108/100)^2}$

∴$\bold\green{10000 \ × \ 108/100 \ × \ 108/100}$

∴$\bold\red{108 \ × \ 108}$

∴$\bold\blue{11664}$

Correct Answer

$\bold{option \ 2 \ ₹11664}$

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Points to remember

We have use formula Amount=P(1+R/100)^n.

P stands for principal

R stands for Rate

T or n stands for time