Question

How long will it take for ₹15000 invested at 15% per annum simple interest to amount to ₹ 21750?

Answer 1

Given :

• Principal = Rs.15000
• Rate = 15 %
• Amount = Rs.21750

To Find :

• Time = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

$\qquad \; {\red{\bigstar \; \; {\green{\underbrace{\underline{\purple{\sf{ Simple \; Interest = Amount - Principal }}}}}}}}$

$\qquad \; {\red{\bigstar \; \; {\green{\underbrace{\underline{\purple{\sf{ Time = \bigg\{ \dfrac{ Simple \; Interest \times 100 }{ Principal \times Rate } \bigg\} }}}}}}}}$

$\dag$ Calculating the Simple Interest :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Simple \; Interest = Amount - Principal } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Simple \; Interest = 21750 - 15000 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Simple \; Interest = Rs. \; 6750 }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Time :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Time = \bigg\{ \dfrac{ Simple \; Interest \times 100 }{ Principal \times Rate } \bigg\} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Time = \bigg\{ \dfrac{ 6750 \times 100 }{ 15000 \times 15 } \bigg\} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Time = \bigg\{ \dfrac{ 675000 }{ 225000 } \bigg\} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Time = \cancel\dfrac{ 675000 }{ 225000 } } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Time = 3 \; years }}}}} \; {\pink{\pmb{\bigstar}}} \\ \\ \\ \\ \end{gathered}$

$\therefore \;$ The Time is 3 years .

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Answer 2

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Initial amount=15,000

Amount after 5 years=19,500

So interest=19,500–15000=4,500

Interest per year=4,500/5=900

Principal amount=15,000

Interest per year=900

Rate of interest=(900÷15000)×100=6%