# Concepts Of Simple Interest

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Simple interest concepts also helps in solving the problems related to that of compound interest also. All questions based on Simple interest can be solved using only one basic formula.

## Some Important Terms In Simple Interest

### Principle

It is the borrowed money and is denoted by P.

### Interest or Simple Interest

The additional amount paid for only borrowed money is Interest and is represented by I or SI

### Time

Money is borrowed for a certain time period, this time period is taken as interest time and is denoted by T or t.

### Amount

Principle along with SI becomes amount and is denoted by A.
Amount =Principle + SI

### Rate

It is the amount charged on principle by the lender for using the money.

## Basic Formulas Of Simple Interest Concepts

\begin{align*}
SI \ =\dfrac {Principle\times Time\times Rate}{100} \\ \\ =\dfrac {P\times T\times R}{100}
\end{align*}

#### Note

• If SI is payable half-yearly then,
consider the rate of SI as half and time as twice
• If SI is payable quarterly then, consider R=R/4 and T=4 times

## Some Important Formulas in Concepts of Simple Interest

• If SI is n times of principle then RT=(n-1) x 100.
• If an amount is n times of certain sum then RT=(n-1) x 100
• If there are different rates R1%,R2%, R3%…..for different time periods t1,t2,t3……then,

\begin{align*} SI=\dfrac {P\left( R_{1}t_{1}+R_{2}t_{2}+R_{3}t_{3}+\ldots \right) }{100}
\end{align*}

• The difference between two SI for a sum of P1, time period T1 at rate R1 and another sum P2, time period T2, rate R3 is \begin{align*}
SI =\dfrac {P_{2}T_{2}R_{2}-P_{1}T_{1}R_{1}}{100} \end{align*}
• When difference between two SI at different rates and times is given as x then,
Principle (P) is

\begin{align*}
\dfrac {x\times 100}{\begin{pmatrix}
Difference \\ in \ rate \end{pmatrix} \times \begin{pmatrix} Difference \\ in \ time
\end{pmatrix}}\end{align*}

• If a principle amounts to x1 in t years at some rate and the resultant new sum now as principle amounts to x2 in t years at another rate then

Principle ( P) is

\begin{align*}
\dfrac {\begin{pmatrix}
Difference \\ in \ amount\end{pmatrix}\times 100}
{\begin{pmatrix}
Difference \\ in \ SI \ rate \end{pmatrix} \times t}
\end{align*}