Question

Find the amount and compound interest on
1: Rs 12000 in 2years at 8% per anumm
2:Rs 20,000 in 2years at 10% per annum ​

Answer 1

i) Principal = 12000

Time = 2 years

Rate of interest = 8% p.a.

Formula :

$\tt{Amount \implies Principal \times{( 1 + \dfrac{R}{100})}^{time}}$

Putting up the values :

$\tt{ Amount \implies 12000 \times {(1 + \dfrac{8}{100})}^{2}}$

$\tt{Amount \implies 12000 \times {(\dfrac{108}{100})}^{2}}$

$\tt{Amount \implies 12000 \times {(\dfrac{27}{25})}^{2}}$

$\tt{Amount \implies 12000 \times \dfrac{27}{25} \times \dfrac{27}{25}}$

$\tt{Amount \implies \cancel{12000} \times \dfrac{27}{25} \times \dfrac{27}{\cancel{25}}}$

$\tt{Amount \implies 480 \times \dfrac{27}{25} \times 27}$

$\tt{Amount \implies 19.2 \times 27 \times 27}$

$\tt{Amount \implies 13996.8}$

Compound Interest : Amount - Principal

=> 13996 (-) 12000

=> 1996

_________________

ii) Principal = 20000

Time = 2 years

Rate of interest = 10% p.a.

Formula :

$\tt{Amount \implies Principal \times{( 1 + \dfrac{R}{100})}^{time}}$

Putting up the values :

$\tt{Amount \implies Principal \times {(1 + \dfrac{R}{100})}^{time}}$

$\tt{Amount \implies 20000 \times {(1 + \dfrac{10}{100})}^{2}}$

$\tt{Amount \implies 20000 \times {(\dfrac{110}{100})}^{2}}$

$\tt{Amount \implies 20000 \times {(\dfrac{11}{10})}^{2}}$

$\tt{Amount \implies 20000 \times \dfrac{11}{10} \times \dfrac{11}{10}}$

$\tt{Amount \implies \cancel{20000} \times \dfrac{11}{10} \times \dfrac{11}{\cancel{10}} }$

$\tt{Amount \implies \cancel{2000} \times \dfrac{11}{\cancel{10}} \times 11}$

$\tt{Amount \implies 200 \times 11 \times 11}$

$\tt{Amount \implies 200 \times 121}$

$\tt{Amount \implies 24200}$

Compound Interest = Amount (-) Principal

=> 24200 - 20000

=> 4200

Steps followed :

1. Firstly we have noted down the formula of Compound Interest.
2. Then taking up the values of Principal and Time and Rate of Interest in the correct places ; we have further solved it.
3. Finally when we got the amount ; to find the compound Interest ; we had to subtract Amount from principal amount.

Simple Interest :

$\tt{ SI \implies \dfrac{P \times R \times T}{100}}$

Answer 2

Step-by-step explanation:

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Glorious31

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i) Principal = 12000

Time = 2 years

Rate of interest = 8% p.a.

Formula :

\tt{Amount \implies Principal \times{( 1 + \dfrac{R}{100})}^{time}}

Putting up the values :

\tt{ Amount \implies 12000 \times {(1 + \dfrac{8}{100})}^{2}}

\tt{Amount \implies 12000 \times {(\dfrac{108}{100})}^{2}}

\tt{Amount \implies 12000 \times {(\dfrac{27}{25})}^{2}}

\tt{Amount \implies 12000 \times \dfrac{27}{25} \times \dfrac{27}{25}}

\tt{Amount \implies \cancel{12000} \times \dfrac{27}{25} \times \dfrac{27}{\cancel{25}}}

\tt{Amount \implies 480 \times \dfrac{27}{25} \times 27}

\tt{Amount \implies 19.2 \times 27 \times 27}

\tt{Amount \implies 13996.8}

Compound Interest : Amount - Principal

=> 13996 (-) 12000

=> 1996

_________________

ii) Principal = 20000

Time = 2 years

Rate of interest = 10% p.a.

Formula :

\tt{Amount \implies Principal \times{( 1 + \dfrac{R}{100})}^{time}}

Putting up the values :

\tt{Amount \implies Principal \times {(1 + \dfrac{R}{100})}^{time}}

\tt{Amount \implies 20000 \times {(1 + \dfrac{10}{100})}^{2}}

\tt{Amount \implies 20000 \times {(\dfrac{110}{100})}^{2}}

\tt{Amount \implies 20000 \times {(\dfrac{11}{10})}^{2}}

\tt{Amount \implies 20000 \times \dfrac{11}{10} \times \dfrac{11}{10}}

\tt{Amount \implies \cancel{20000} \times \dfrac{11}{10} \times \dfrac{11}{\cancel{10}} }

\tt{Amount \implies \cancel{2000} \times \dfrac{11}{\cancel{10}} \times 11}

\tt{Amount \implies 200 \times 11 \times 11}

\tt{Amount \implies 200 \times 121}

\tt{Amount \implies 24200}

Compound Interest = Amount (-) Principal

=> 24200 - 20000

=> 4200

Steps followed :

Firstly we have noted down the formula of Compound Interest.

Then taking up the values of Principal and Time and Rate of Interest in the correct places ; we have further solved it.

Finally when we got the amount ; to find the compound Interest ; we had to subtract Amount from principal amount.

Simple Interest :

st=P*R*T/100