Question

Que. 5. Calculate if 10,000 is invested at interest rate of 12% per
annum, what is the amount after 3 years if the compounding of
interest is done?​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Principle = Rs. 10,000
• Rate = 12%
• Time = 3 years

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• CI = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{Amount = P \bigg\lgroup 1 + \dfrac{rate}{100}\bigg\rgroup^{time}}}}}$

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$\sf :\implies\: {\bold{ Amount = 10000 \bigg\lgroup 1 + \dfrac{12}{100} \bigg\rgroup^{3} }}$

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$\sf :\implies\: {\bold{ Amount = 10000 \bigg\lgroup \dfrac{100 + 12 }{100} \bigg\rgroup^{3} }}$

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$\sf :\implies\: {\bold{ Amount = 10000 \bigg\lgroup \dfrac{112 }{100} \bigg\rgroup^{3} }}$

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$\sf :\implies\: {\bold{ Amount = 10000\times \dfrac{112\times 112\times 112}{100\times 100\times 100}}}$

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$\sf :\implies\: {\bold{ Amount = 1000\times \dfrac{112\times 112\times 112}{100\times 100\times 10}}}$

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$\sf :\implies\: {\bold{ Amount = 100\times \dfrac{112\times 112\times 112}{100\times 100}}}$

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$\sf :\implies\: {\bold{ Amount = 10\times \dfrac{112\times 112\times 112}{100\times 10}}}$

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$\sf :\implies\: {\bold{ Amount = \dfrac{112\times 112\times 112}{100}}}$

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$\sf :\implies\: {\bold{ Amount = \dfrac{12544\times 112}{100}}}$

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$\sf :\implies\: {\bold{ Amount ={1404928}{100}}}$

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$\sf :\implies\: {\bold{ Amount = Rs. 14049.28}}$

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$\sf{\red{\boxed{\bold{CI = Amount - Principle }}}}$

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$\sf :\implies\: {\bold{ CI = Rs. 14049.28 - Rs. 10000}}$

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$\sf :\implies\: {\bold{CI = Rs.4049.28 }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Rs. 10000 will earn Rs. 4049.28 as Compound Interest in 3 years at 12% per annum compounded annually

Answer 2

Answer:

Given :-

• Principal (P) = Rs 10000
• Rate of Interest (r%) = 12 %
• Time (n) = 3 years

To Find :-

• What is the compound interest (C.I)

Formula Used :-

❶ To find amount we know that,

$\boxed{\bold{\small{A\: = P(1\: +\: \dfrac{r}{100})^{n}}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time

❷ To find compound interest we know that,

$\boxed{\bold{\small{Compound\: Interest\: =\: Amount\: -\: Principal}}}$

Solution :-

❶ First we have to find the amount,

Given :

◆ P = Rs 10000

◆ R% = 12 %

◆ n = 3 years

According to the question by using the formula we get,

↦ A = 10000( 1 + $\dfrac{12}{100}$ )³

↦ A = 10000( $\dfrac{112}{100}$ )³

↦ A = 10000 × $\dfrac{112}{100} × \dfrac{112}{100} × \dfrac{112}{100}$

↦ A = $\dfrac{112 × 112 × 112}{100}$

↦ A = $\dfrac{1404928}{100}$

➠ A = 14049.28

$\therefore$ The amount after 3 years will be Rs 140449.28 .

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❷ Now, we have to find the Compound interest,

⇒ C.I = 14049.28 - 10000

➥ $\small\bf{\underbrace{\green{C.I\: =\: 4049.28}}}$

$\therefore$ The compound interest is Rs 4049.28.

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