Question

Find the amount and compound interest in rs.12,000in 2 years at 8%pa

Answer 1

Given

• Principal = ₹12000.
• Rate of Interest = 8% p.a.
• Time = 2 years.

To Find

• Amount.
• Compound Interest.

Solution

Calculating Amount

When P = Principal, R = Rate of Interest per annum and n = Number of years is given then the formula for A = Amount is:-

$\bigstar \:\:\boxed{\sf{A = P\bigg\lgroup1+ \frac{R}{100}\bigg\rgroup}^n}$

Substituting known values

$\sf\longmapsto{A = 12000\bigg\lgroup1+ \dfrac{8}{100}\bigg\rgroup^2} \\ \\ \\ \sf\longmapsto{A = 12000 \bigg \lgroup1 + \frac{2}{25} \bigg \rgroup^{2} } \\ \\ \\ \sf\longmapsto{A = 12000 \bigg \lgroup \frac{25 + 2}{25} \bigg \rgroup^{2}} \\ \\ \\\sf\longmapsto{A = 12000 \bigg \lgroup \frac{27}{25} \bigg \rgroup ^{2}} \: \: \: \: \: \: \: \: \\ \\ \\\sf\longmapsto{A = \cancel{12000} \times \frac{27}{ \cancel{25}} \times\frac{27}{25}} \\ \\ \\\sf\longmapsto{A= \frac{480\times27\times27}{25}} \: \: \: \: \: \: \\ \\ \\\sf\longmapsto{A =19.2 \times 27 \times 27} \: \: \: \: \: \: \\ \\ \\\sf\therefore \underline{\boxed{\sf{Amount= ₹13996.8}}}$

$\:$

Calculating Compound Interest

When A = Amount and P = Principal is given then the formula for C.I. = Compound Interest is:-

$\bigstar \:\:\boxed{\sf{C.I. = Amount\:-Principal}}$

Substituting known values

$\sf \longmapsto{C.I.=₹13996.8 - ₹12000} \\ \\ \\ \sf \therefore \underline{\boxed{\sf{Compound \: Interest = ₹1996.8}}}$

$\:$

Final Answer

• Amount = ₹13,996.8.
• Compound Interest = ₹1,996.8.

Additional Information

If P = Principal, R = Rate of Interest per annum, n = Number of years and A = Amount then formula for A = Amount is:-

$\sf{A = P\bigg\lgroup1 + \dfrac{R}{100}\bigg\rgroup}^n \\ \\\sf\: [When \: Interest\:is\: Compounded \: annually]$

$\:$

$\sf{A = P\bigg\lgroup1 + \dfrac{R}{200}\bigg\rgroup}^{2n}\\ \\\sf\: [When \: Interest\:is\: Compounded \:halfyearly]$

$\:$

$\sf{A = P\bigg\lgroup1 + \dfrac{R}{400}\bigg\rgroup}^{4n}\\ \\\sf\: [When \: Interest\:is\: Compounded \:quarterly]$

$\:$

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Answer 2

Step-by-step explanation:

Given :

• Principal = 12000

• Time = 2 years

• Rate of interest = 8% p.a.

Formula used :

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

Putting the values :

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

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

$\bf{Amount \implies 12000 \times {(\dfrac{27}{25})}^{2}} \\ \\ \bf{Amount \implies 12000 \times \dfrac{27}{25} \times \dfrac{27}{25}} \\ \\ \bf{Amount \implies \cancel{12000} \times \dfrac{27}{25} \times \dfrac{27}{\cancel{25}}} \\ \\ \bf{Amount \implies 480 \times \dfrac{27}{25} \times 27} \\ \\ \bf{Amount \implies 19.2 \times 27 \times 27} \\ \\ \bf{Amount \implies 13996.8}$

Compound Interest :

Amount - Principal

= 13996 - 12000

= 1996