Question

7. Pranay deposited ? 5500 in a bank for 2 years. The bank pays 5% interest per annum. What amount did he get back after 2 years ?​

Answer 1

Answer:

Given :

• $\small{\bull}$ Principle = Rs.5500
• $\small{\bull}$ Time = 2 years
• $\small{\bull}$ Rate of Interest = 5% per annum.

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

To Find :

• $\small{\bull}$ Amount after 2 years

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

Using Formulas :

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

Where :-

• $\tiny{\bull}$ A = Amount
• $\tiny{\bull}$ P = Principle
• $\tiny{\bull}$ R = Rate
• $\tiny{\bull}$ T = Time

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

Solution :

★ Finding the amount by substituting the values in the formula :-

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

$\dashrightarrow{\sf{A= 5500\bigg(1 + \dfrac{ {5}}{100} \bigg)^{2}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{(1 \times 100) + (5 \times 1)}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{100 + 5}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{105}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 5500\bigg( \cancel{\dfrac{105}{100}} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 5500\bigg({\dfrac{21}{20}} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{21}{20} \times \dfrac{21}{20} \bigg)}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{21 \times 21}{20 \times 20}\bigg)}}}$

${\dashrightarrow{\sf{A= 5500\bigg(\dfrac{441}{400}\bigg)}}}$

${\dashrightarrow{\sf{A= 5500 \times \dfrac{441}{400}}}}$

${\dashrightarrow{\sf{A= \dfrac{5500 \times 441}{400}}}}$

${\dashrightarrow{\sf{A= \dfrac{2425500}{400}}}}$

${\dashrightarrow{\sf{A = Rs.6063.75}}}$

$\bigstar \: \underline{\boxed{\sf{\pink{Amount= Rs.6063.75}}}}$

∴ Pranay will get Rs.6053.75 after 2 years.

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

Learn More :

$\longrightarrow\small{\underline{\boxed{\sf{\purple{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Amount = Principle + Interest}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{ Principle=Amount - Interest }}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{Time = \dfrac{Simple \: Interest \times 100}{Principle \times Rate}}}}}}$

$\underline{\rule{220pt}{2.5pt}}$