Question

Calculate the amount and compound interest of Rs 4600 in 2 years when the rate of interest of successive years are 10 % and 20 % respectively (solve it without using formula)

Solve it fast its urgent plz​

Answer 1

Solution!!

The concept of compound interest has to be used here.

First year:-

Principal (P) = Rs 4600

Time (T) = 1 year

Rate of interest (R) = 10%

Interest = (P × R × T)/100

Interest = (4600 × 10 × 1)/100

Interest = 46 × 10 × 1

Interest = Rs 460

Amount = Principal + Interest

Amount = Rs 4600 + Rs 460

Amount = Rs 5060

Second year:-

The amount in the first year becomes principal in the second year.

Principal (P) = Rs 5060

Time (T) = 1 year

Rate of interest (R) = 20%

Interest = (P × R × T)/100

Interest = (5060 × 20 × 1)/100

Interest = 506 × 2 × 1

Interest = Rs 1012

Amount = Principal + Interest

Amount = Rs 5060 + Rs 1012

Amount = Rs 6072

Compound Interest (CI) = Final amount - Principal in the first year

CI = Rs 6072 - Rs 4600

CI = Rs 1472

Answer 2

Answer:

$\begin{gathered}\huge{\textbf{\textrm{\underline{\underline{\color{green}{Question:-}}}}}}\end{gathered}$

● Calculate the amount and compound interest of Rs 4600 in 2 years when the rate of interest of successive years are 10 % and 20 % respectively..

$\begin{gathered}\huge{\textbf{\textrm{\underline{\underline{\color{green}{Solution:-}}}}}}\end{gathered}$

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

• $\dashrightarrow\sf{Principle = Rs.4600}$
• $\dashrightarrow\sf{Time = 2 \: years}$
• $\dashrightarrow \sf{Rate \: {R_1}= 10 \%}$
• $\dashrightarrow \sf{Rate \: {R_2}= 20 \%}$

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

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

• $\dashrightarrow \sf{Amount \: and \: compound \: interest }$

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

$\begin{gathered}\large{\textsf{\textbf{\underline{\underline{\color{brown}{Formula Used:}}}}}}\end{gathered}$

${\Large{\dag}}{\underline{\boxed{\sf{Amount ={P{\bigg(1 +\dfrac{R_1}{100}\bigg)} {\bigg(1 +\dfrac{R_2}{100}\bigg)}}}}}}$

$\dag{\underline{\boxed{\sf{Compound \: Interest = Amount- Principle }}}}$

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

$\begin{gathered}\large{\textsf{\textbf{\underline{\underline{\color{brown}{Full Solution:}}}}}}\end{gathered}$

$\bigstar \: {\underline{\pmb{\frak{\red{Finding \: the \: Amount}}}}}$

$\quad{: \implies{\sf{Amount = \bf{P{\bigg(1 +\dfrac{R_1}{100}\bigg)} {\bigg(1 +\dfrac{R_2}{100}\bigg)}}}}}$

• Substituting the values

$\quad{: \implies{\sf{Amount = \bf{4600{\bigg(1 +\dfrac{10}{100}\bigg)} {\bigg(1 +\dfrac{20}{100}\bigg)}}}}}$

$\quad{: \implies{\sf{Amount = \bf{4600{\bigg(1 \times 100 +\dfrac{10}{100}\bigg)} {\bigg(1 \times 100 +\dfrac{20}{100}\bigg)}}}}}$

$\quad{: \implies{\sf{Amount = \bf{4600{\bigg(\dfrac{100 + 10}{100}\bigg)} {\bigg(\dfrac{100 + 20}{100}\bigg)}}}}}$

$\quad{: \implies{\sf{Amount = \bf{4600{\bigg(\dfrac{110}{100}\bigg)} {\bigg(\dfrac{120}{100}\bigg)}}}}}$

$\quad{: \implies{\sf{Amount = \bf{4600 \times {\dfrac{110}{100}} \times {\dfrac{120}{100}}}}}}$

$\quad{: \implies{\sf{Amount = \bf{\dfrac{4600 \times 110 \times 120}{100 \times 100}}}}}$

$\quad{: \implies{\sf{Amount = \bf{\dfrac{60720000}{10000}}}}}$

$\quad{: \implies{\sf{Amount=\bf{\cancel{\dfrac{60720000}{10000}}}}}}$

$\quad{: \implies{\sf{Amount = \bf{Rs.6072}}}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{red}{Amount = {Rs.6072}}}}}}}\end{gathered}$

• Hence, The Amount is Rs.6072

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

$\bigstar \: {\underline{\pmb{\frak{\red{Finding \: the \: Compound \: Interest }}}}}$

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

• Substituting the values

$\quad{: \implies{\sf{Compound \: Interest = \bf{6072-4600}}}}$

$\quad{: \implies{\sf{Compound \: Interest =\bf{Rs.1472}}}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{red}{Compound Interest = Rs.1472}}}}}}\end{gathered}$

• Henceforth,The Compound Interest is Rs.1472.

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

$\begin{gathered}\large{\textsf{\textbf{\underline{\underline{\color{brown}{Answer:}}}}}}\end{gathered}$

• ● The Amount is Rs.6072.
• ● The Compound Interest is Rs.1472.

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

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

★ Formula of Principle(P) if Amount and Interest given

$\odot{\boxed{\sf{\purple{P=Amount - Interest}}}}$

★ Formula of Principle (P) if Interest,time and rate given

$\odot{\boxed{\sf{\purple{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

★ Formula of Principle (P) if amount,time and rate given

$\odot{\boxed{\sf{\purple{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

★ Formula of Amount if Principle (P) and Interest (I) given

${\odot{\boxed{\sf{\purple{Amount = Principle + Interest }}}}}$