Question

Find the amount and compound interest on
1- Rs 12000 in 2 years at 8% per annum
​

Answer 1

Answer:

• Principal = Rs. 12000
• Rate = 8% per annum
• Time = 2 years

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}\\\\\\:\implies\sf Amount = 12000 \times \bigg(1 +\dfrac{8}{100}\bigg)^{2}\\\\\\:\implies\sf Amount = 12000 \times \bigg(\dfrac{100 + 8}{100}\bigg)^{2}\\\\\\:\implies\sf Amount = 12000 \times \bigg(\dfrac{108}{100}\bigg)^{2}\\\\\\:\implies\sf Amount = 12000 \times \dfrac{108}{100} \times \dfrac{108}{100}\\\\\\:\implies\sf Amount = 1.2\times 108 \times 108\\\\\\:\implies\sf Amount = 1.2\times 11664\\\\\\:\implies\sf Amount = Rs.\:13996.8$

⠀

$\therefore\:\underline{\textsf{Hence, Amount after 2 years is \textbf{Rs. 13,996.8}}}.$

$\rule{200}{1}$

Compound Interest :

$\dashrightarrow\sf Compound\:Interest=Amount-Principal\\\\\\\dashrightarrow\sf Compound\:Interest= Rs.\:13996.8-Rs.\:12000\\\\\\\dashrightarrow\sf Compound\:Interest=Rs.\:1996.8$

⠀

$\therefore\:\underline{\textsf{Compound Interest after 2 years is \textbf{Rs. 1,996.8}}}.$

Answer 2

Step-by-step explanation:

★ Concept :-

Here the concept of Amount and Compound Interest has been used. As we see that we are given the Principal, Time, and the Rate of Interest. So first, we will find out the Amount. After that, using the formula of Compound Interest we will easily find out the Compound Interest by applying the required values.

Let's do it !!!

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★ Formula Used :-

$\star\;\underline{\boxed{\bf{\pink{A\ =\ P \times \bigg (1\ +\ \dfrac{r}{100} \bigg)^t}}}}$

$\star\;\underline{\boxed{\bf{\pink{C.I\ =\ Amount\ -\ Principal}}}}$

___________________

★ Solutions :-

Given,

» Principal, P = Rs. 12000.

» Rate, r = 8% per annum.

» Time, t = 2 years.

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~ For the value of Amount ::

‎

We know that,

‎

$\sf : \implies {Amount\ =\ \bf P \times \bigg (1\ +\ \dfrac{r}{100} \bigg)^t}$

‎

~ By applying the values we get :-

‎

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

‎

$\sf : \implies {Amount\ =\ \bf 12000 \times \bigg (\dfrac{100\ +\ 8}{100} \bigg)^2}$

‎

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

‎

$\sf : \implies {Amount\ =\ \bf \cancel {12000} \times \dfrac{108}{\cancel {100}} \times \dfrac{208}{\cancel {100}}}$

‎

$\sf : \implies {Amount\ =\ \bf 1.2 \times 108 \times 108}$

‎

$\sf : \implies {Amount\ =\ \bf 1.2 \times 11664}$

‎

$\bf : \implies {Amount\ =\ {\red {Rs.\ 13996.8.}}}$

‎

∴ Hence, the Amount is Rs. 13996.8.

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~ For the value of Compound Interest ::

‎

We know that,

‎

$\sf : \implies {Compound\ Interest\ =\ \bf Amount\ -\ Principal}$

‎

~ By applying the values, we get :-

‎

$\sf : \implies {Compound\ Interest\ =\ \bf 13996.8\ -\ 12000}$

‎

$\bf : \implies {Compound\ Interest\ =\ {\orange {Rs.\ 1996.8.}}}$

‎

∴ Hence, the Compound Interest is Rs. 1996.8.

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★ More to know :-

‎

$\sf \leadsto {S.P\ =\ \bigg (\dfrac{100\ +\ Profit \%}{100} \bigg) \times 100.}$

‎

$\sf \leadsto {C.P\ =\ \dfrac{S.P \times 100}{100\ +\ Profit \%}.}$

‎

$\sf \leadsto {Profit\ =\ \dfrac{Profit \% \times C.P}{100}.}$

‎

$\sf \leadsto {Profit \% \ =\ \dfrac{Profit}{C.P} \times 100.}$