Question

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Answer 1

Question :

• I took a loan of Rs.30,000 from a finance company. If the rate of interest is 7% per annum compounded annually, calculate the amount I have to pay after two years .

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Step-by-step explanation:

$\large\bigstar \underline{ \blue{\frak{Given \: information} - - }}$

• Principal = Rs.30,000
• Rate of interest = 7%
• Time = 2 years

$\large \bigstar \underline{ \blue{ \frak{Need \: to \: Find \: out - - - }}}$

• we need to Find amount we have to pay after 2 years ?

$\large \bigstar \underline{ \orange{ \frak{Solution - - - - }}}$

Calculating Compound Interest

• Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

The formula for calculating compound interest is as follows:

$\longrightarrow \pink{ \large \fbox{\boxed{ \bf \: A = P \bigg \lgroup1 + \frac{r}{100} { \bigg \rgroup}^{t} }}}$

where ,

▪︎A = Amount

▪︎P = principal

▪︎R = rate of interest

▪︎T = time

$\sf \underline{ \blue{Now \: putting \: values \: in \: formula }}$

$\\ \longmapsto \bf \: A = P \bigg \lgroup1 + \frac{r}{100} { \bigg \rgroup}^{t}$

$\\ \longmapsto \: \bf \: A = 30000 \bigg \lgroup1 + \frac{7}{100} { \bigg \rgroup}^{2}$

$\\ \longmapsto \: \bf \: A = 30000 \bigg \lgroup100 + \frac{7}{100} { \bigg \rgroup}^{2}$

$\\ \longmapsto \: \bf \: A = 30000 \bigg \lgroup \frac{107}{100} { \bigg \rgroup}^{2}$

$\\ \longmapsto \: \bf \: A = 3 \cancel{00} \cancel{00 } \times \frac{107}{ \cancel{100}} \times \frac{107}{ \cancel{100}}$

$\\ \longmapsto \: \bf \: A = 3 \times 107 \times 107$

$\\ \longmapsto \: \bf \: A = 321 \times 107$

$\\ \fbox{\boxed{ \large \longmapsto \: \frak{\: Amount =34347 } }}$

$\bigstar \fbox{ \boxed{\sf \orange {\: Hence \: we \: will \: pay \: amount \: after \: 2 \: years = 34347 }}} \bigstar$

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Answer 2

Answer:

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Given :}}}}}}}\end{gathered}$

• ↠ Principle = Rs.30000
• ↠ Rate of Interest = 7%
• ↠ Time = 2 years

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:To Find :}}}}}}}\end{gathered}$

• ↠ Amonut which I have to pay after two years.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Concept :}}}}}}}\end{gathered}$

⊙ Here we have given that the Principal is ₹30000, Time is 2 years and rate is 7 p.c.p.a. Here we need to find out the amount.

⊙ So, for finding amonut we will insert the values in the formula.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Using Formula :}}}}}}}\end{gathered}$

$\quad\bigstar{\underline{\boxed{\sf{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\red\bigstar$ Where :-

• ↠ A = Amount
• ↠ P = Principle
• ↠ R = Rate of Interest
• ↠ T = Time

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Solution :}}}}}}}\end{gathered}$

$\red\bigstar$ Here :-

• ↠ Principle = Rs.30000
• ↠ Rate of Interest = 7%
• ↠ Time = 2 years

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Finding the amount :-

$\quad{\dashrightarrow\pmb{\sf{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{A ={30000{\bigg(1 + \dfrac{7}{100}{\bigg)}^{2}}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000{\bigg( \dfrac{( 1\times 100) + (7 \times 1)}{100}{\bigg)}^{2}}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000{\bigg( \dfrac{ 100 + 7}{100}{\bigg)}^{2}}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000{\bigg( \dfrac{ 107}{100}{\bigg)}^{2}}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000{\bigg( \dfrac{ 107}{100} \times \dfrac{ 107}{100}\bigg)}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000{\bigg( \dfrac{11449}{10000}\bigg)}}}}}$

$\quad{\dashrightarrow{\sf{A ={30000 \times \dfrac{11449}{10000}}}}}$

$\quad{\dashrightarrow{\sf{A ={ \cancel{30000} \times \dfrac{11449}{\cancel{10000}}}}}}$

$\quad{\dashrightarrow{\sf{A ={3 \times 11449}}}}$

$\quad{\dashrightarrow{\sf{A ={Rs.34347}}}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\purple{Amount={Rs.34347}}}}}}}$

∴ Rs.34347 amonut I have to pay after two years.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Learn More :}}}}}}}\end{gathered}$

$\quad{\longrightarrow{\sf{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

$\quad{\longrightarrow{\sf{Amount = Principle + Interest}}}$

$\quad{\longrightarrow{\sf{ P=Amount - Interest }}}$

$\quad{\longrightarrow{\sf{ S.I = \dfrac{P \times R \times T}{100}}}}$

$\quad{\longrightarrow{\sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}$

$\quad{\longrightarrow{\sf{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}$

$\quad{\longrightarrow{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}$

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