Question

Find the amount to be paid at the end of 3 years in each case:

(a) Principal = Rs 1,200 at 12% p.a.

(b) Principal = Rs 7,500 at 5% p.a. ​

Answer 1

Answer:

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Answer 2

Answer:

Question :

Find the amount to be paid at the end of 3 years in each case:

• → (a) Principal = Rs 1,200 at 12% p.a.
• → (b) Principal = Rs 7,500 at 5% p.a.

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

Required Formulas :

Let us know the required formulas to solve the questions :

Formula of simple interest :

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

• → S.I = Simple Interest
• → P = Principle
• → R = Rate
• → T = Time

Formula of Amount :

${\longrightarrow{\small{\underline{\boxed{\sf{A = P + S.I}}}}}}$

• → A = Amount
• → P = Principle
• → R = Rate
• → T = Time

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

Solution :

(a) Principal = Rs 1,200 at 12% p.a.

✏ Firstly, calculating the Simple Interest :

$\longrightarrow\small{\sf{S.I= \dfrac{1200\times 12\times 3}{100}}}$

$\longrightarrow\small{\sf{S.I= \dfrac{1200\times 36}{100}}}$

$\longrightarrow\small{\sf{S.I= \dfrac{43200}{100}}}$

$\longrightarrow\small{\sf{S.I= \cancel{\dfrac{43200}{100}}}}$

$\longrightarrow\small{\sf{S.I=Rs.432 }}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{S.I=Rs.432 }}}}}$

✒ Now, calculating the Amount :

${\longrightarrow{\small{\sf{A = P + S.I}}}}$

${\longrightarrow{\small{\sf{A = 1200 + 432}}}}$

${\longrightarrow{\small{\sf{A = Rs.1632}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\pink{Amount= Rs.1632}}}}}}}$

∴ The amount is Rs.1632.

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(b) Principal = Rs 7,500 at 5% p.a.

✏ Firstly, calculating the Simple Interest :

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

$\longrightarrow\small{\sf{S.I= \dfrac{7500\times 5\times 3}{100}}}$

$\longrightarrow\small{\sf{S.I= \dfrac{7500\times 15}{100}}}$

$\longrightarrow\small{\sf{S.I= \dfrac{112500}{100}}}$

$\longrightarrow\small{\sf{S.I= \cancel{\dfrac{112500}{100}}}}$

$\longrightarrow\small{\sf{S.I= Rs.1125}}$

$\longrightarrow\small{\underline{\boxed{\sf{\purple{S.I=Rs.1125 }}}}}$

✒ Now, calculating the Amount :

${\longrightarrow{\small{\sf{A = P + S.I}}}}$

${\longrightarrow{\small{\sf{A = 7500 + 1125}}}}$

${\longrightarrow{\small{\sf{A = Rs.8625}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\pink{Amount= Rs.8625}}}}}}}$

∴ The amount is Rs.8625.

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

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.

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

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

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

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

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

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

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

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

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