# Concepts Of Compound Interest

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Compound interest concepts-based problems are frequently asked in most competitive exams. Simple Interest concept also with its basic knowledge makes it easier. Learning squares and cubes of numbers will increase speed in solving the problems.

## Compound Interest Definition

If the interest for each period is added to the principle before the interest for the next period is calculated then, that interest is compound interest and is represented by CI.

## Basic Formula Of Compound Interest Concepts

\begin{equation} Amount \ \left( A\right) =P\left( 1+\dfrac {R}{100}\right) ^{t} \end{equation} \begin{equation}
Compound \ Interest \ \left( CI\right) =Amount-Principle=P\left[ \left( 1+\dfrac {R}{100}\right) ^{t}-1\right] \end{equation} \begin{equation}
Rate \ of \ Interest\left( R\right) =\left[ \left( \dfrac {A}{P}\right) ^{1/t}-1\right] \% \ p\cdot a \end{equation}

## Some Important Formulas in Concepts Of Compound Interest

• At a given rate of interest for 1 year simple and compound interest are same.
• If there are different rates of interests r1%, r2%, r3%…….for different time periods a first year, second year, third year, and so on respectively then, \begin{equation}Amount \ \left( A\right) =P\left( 1+\dfrac {r_{1}}{100}\right) \left( 1+\dfrac {r_{2}}{100}\right) \ldots .. \end{equation}
• The difference between compound and simple interests at a rate of R% per annum for 2 years is \begin{equation}
CI-SI=P\left( \dfrac {R}{100}\right) ^{2}=\dfrac {SI\times R}{200}
\end{equation} \begin{equation} Similarly \ for \ 3 \ years \
\end{equation} \begin{equation}
CI-SI=p\left( \dfrac {R}{100}\right) ^{2}\times \left( 3+\dfrac {R}{100}\right) \end{equation}
• If a principle after t years becomes n times of itself on compound interest then, \begin{equation}
Rate \ of \ Interest \ R\% =\left( n^{1/t}-1\right) \times 100\%
\end{equation}
• If simple interest for a principle after 2 years at a rate of R% is SI then,
\begin{equation} \left( CI\right) =SI\left( 1+\dfrac {R}{200}\right) \end{equation}

### Note

• If interest is due half-yearly then,
consider the rate of interest as half and time as twice then
\begin{equation} Amount \ \left( A\right) =P\left( 1+\dfrac {R/2}{100}\right) ^{2T} \end{equation}
• when interest is due quarterly then, consider R=R/4 and T=4 times then
\begin{equation} Amount \ \left( A\right) =P\left( 1+\dfrac {R/4}{100}\right) ^{4T} \end{equation}
• If interest is due monthly then, consider R=R/12 and T=12 times then \begin{equation} Amount)\ \left( A\right) =P\left( 1+\dfrac {R/12}{100}\right) ^{12T} \end{equation}
• If interest is due yearly then, consider R=R% and T= T times \begin{equation} Amount \ \left( A\right) =P\left( 1+\dfrac {R}{100}\right) ^{T} \end{equation}