Question

Amount of simple interest accrued on an amount of ₹28500 in 7 years is ₹23940. What is the rate of interest p.a.?

Answer 1

Answer :-

Rate of interest = 12 %

Step-by-step explanation :-

Analysing the question,

Given:

• Simple interest = ₹ 23940
• Principal = ₹ 28500
• Time period = 7 years

To find:

Rate of interest per annum = ?

Formula used:

$\maltese \: \: \boxed { \bf{SI = \dfrac{PTR}{100}}}$

where:

• SI is the Simple interest
• P is the principal
• T is the time period
• R is the rate of interest

Solution:

Applying the above formula and substituting the given values,

$\hookrightarrow \: \: \sf{23940 = \dfrac{28500 \times 7 \times R}{100} }$

$\dashrightarrow \: \: \sf{23940 = \dfrac{285 \cancel{00} \times 7 \times R}{ \cancel{100}} }$

$\dashrightarrow \: \: \sf{285 \times 7 \times R = 23940}$

$\dashrightarrow \: \: \sf{1995 \times R = 23940}$

$\dashrightarrow \: \: \sf{R = \dfrac{23940}{1995} }$

$\dashrightarrow \: \: \sf{R = 12}$

$\therefore \boxed{ \underline{ \boldsymbol{Rate \: of \: interest = 12 \%}}}$

Answer 2

Answer:

${\bigstar}\underline{\underline{\textsf{\textbf{ Given\::- }}}}$

• $\leadsto$ Principle = Ra.285000
• $\leadsto$ Simple Interest = Rs.23940
• $\leadsto$ Time = 7 years

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

${\bigstar}\underline{\underline{\textsf{\textbf{ To Find\::- }}}}$

• $\leadsto$ Rate of Interest per annumn

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

${\bigstar}\underline{\underline{\textsf{\textbf{ Using Formula\::- }}}}$

$\begin{gathered} \dag\underline{\boxed{\boxed{\sf{S.I = \dfrac{PTR}{100}}}}}\end{gathered}$

Where

• $\leadsto$ S.I = Simple Interest
• $\leadsto$ P = Principle
• $\leadsto$ T = Time
• $\leadsto$ R = Rate of Interest

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

${\bigstar}\underline{\underline{\textsf{\textbf{ Solution\::- }}}}$

$\begin{gathered} \dashrightarrow {\sf{S.I = \dfrac{P \times T \times R}{100}}}\end{gathered}$

• Substituting the all given values

$\begin{gathered} \dashrightarrow {\sf{23940 = \dfrac{28500 \times 7 \times R}{100}}}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{23940 = \dfrac{199500\times R}{100}}}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{23940} = \dfrac{{\cancel{199500}}\times R}{\cancel{100}}}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{23940} = {1995}\times R}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{\frac{23940}{1995}}= {R}}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{\cancel{\frac{23940}{1995}}}= {R}}\end{gathered}$

$\begin{gathered} \dashrightarrow {\sf{12= R}}\end{gathered}$

$\begin{gathered} \bigstar\underline{\boxed{\sf{R = 12\%}}}\end{gathered}$

$\therefore{\underline{\sf{\red{The \: Rate \: of \: Interest \: is \: 12 \%}}}}$

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

${\bigstar}\underline{\underline{\textsf{\textbf{ Learn More\::- }}}}$

$\small\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$