Question

&I=PXRYT RI year 100 Find the compound interest on the following:principal =₹ 5000 rate%=10% number of years=2​

Answer 1

Answer:

Given :

• ➝ Principle = Rs.5000
• ➝ Rate of Interest = 10%
• ➝ Time = 2 years

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

To Find :

• ➝ Compound Interest

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

Concept :

➝ Here we have given that the Principal is Rs.500, Time is 2 years and Rate is 10 p.c.p.a. As we know that to find the compound interest we need amount. So firstly we will find out the amount.

➝ After finding the Amount we will find out the Compound interest by substituting the values in the formula.

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

Using Formulas :

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

$\longrightarrow\small{\underline{\boxed{\sf{{C.I=A- P}}}}}$

Where :

• ➟ A = Amount
• ➟ P = Principle
• ➟ R = Rate
• ➟ T = Time
• ➟ C.I = Compound Interest

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

Solution :

Finding the amount by substituting the values in the formula :

${\implies{\sf{A= P\bigg[1 + \dfrac{ {R}}{100} \bigg]^{T}}}}$

${\implies{\sf{A= 5000\bigg[1 + \dfrac{10}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \dfrac{(1 \times 100) + (10 \times 1)}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \dfrac{(100) + (10)}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \: \dfrac{110}{100} \: \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \: \cancel{\dfrac{110}{100}} \: \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \: \dfrac{11}{10} \: \bigg]^{2}}}}$

${\implies{\sf{A= 5000\bigg[ \dfrac{11}{10} \times \dfrac{11}{10} \bigg]}}}$

${\implies{\sf{A= 5000\bigg[ \dfrac{11 \times 11}{10 \times 10} \bigg]}}}$

${\implies{\sf{A= 5000\bigg[ \: \dfrac{121}{100} \: \bigg]}}}$

${\implies{\sf{A= 5000 \times \dfrac{121}{100}}}}$

${\implies{\sf{A= \cancel{5000} \times \dfrac{121}{\cancel{100}}}}}$

${\implies{\sf{A= 50 \times 121}}}$

${\implies{\sf{A= Rs.6050}}}$

$\bigstar \: \underline{\boxed{\sf{\purple{A= Rs.6050}}}}$

Hence, the amount is Rs.6050

Finding the compound interest by the values in the formula :

${\implies{\sf{C.I=A- P}}}$

${\implies{\sf{C.I=6050 - 5000}}}$

${\implies{\sf{C.I=Rs.1050}}}$

$\bigstar \: \underline{\boxed{\sf{\purple{C.I=Rs.1050}}}}$

Hence, the compound interest is Rs.1050.

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

Learn More :

»» Principal: Money which is taken or given in the form of loan. That's called the principal. It is denoted by P.

»» Time: The period for which the loan is taken or given is called time. It is expressed by T or t.

»» Rate: The rate at which interest is charged or paid is called interest rate. It is denoted by r or R.

»» Interest: In addition to the principal amount, which is refunded, interest is paid. It is denoted by I.

»» Amount: For example, money taken is called principal and money returned is called compound.

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

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

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

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

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

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

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

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

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

Answer 2

Step-by-step explanation:

Enclosure provides the solution.