\displaystyle \textbf{Introduction to Simple Interest and Compound Interest}
\displaystyle \text{Before studying simple and compound interest, we first understand some}
\displaystyle \text{important terms used in interest calculations.}
\displaystyle \\
\displaystyle \textbf{Principal}
\displaystyle \text{The money borrowed, lent or invested for a certain period of time is}
\displaystyle \text{called the principal or principal sum. It is usually denoted by }P.
\displaystyle \\
\displaystyle \textbf{Interest}
\displaystyle \text{Interest is the additional money paid by a borrower to a lender for the}
\displaystyle \text{use of the principal for a specified period of time.}
\displaystyle \text{It may also be the money earned on an investment or deposit.}
\displaystyle \\
\displaystyle \textbf{Amount}
\displaystyle \text{The total money received or paid at the end of the specified period is}
\displaystyle \text{called the amount. It is usually denoted by }A.
\displaystyle \text{Amount}=\text{Principal}+\text{Interest}.
\displaystyle A=P+I.
\displaystyle \\
\displaystyle \textbf{Rate of Interest}
\displaystyle \text{The interest payable on Rs. }100\text{ of principal for a unit period is}
\displaystyle \text{called the rate of interest. It is expressed as a percentage.}
\displaystyle \text{When the unit period is one year, it is called the rate per annum,}
\displaystyle \text{abbreviated as p.a. Thus, }8\%\text{ p.a. means Rs. }8\text{ interest}
\displaystyle \text{per year on every Rs. }100\text{ of principal.}
\displaystyle \\
\displaystyle \textbf{Time}
\displaystyle \text{The period for which money is borrowed, lent or invested is called time.}
\displaystyle \text{When the rate of interest is per annum, time must normally be expressed}
\displaystyle \text{in years while applying the interest formula.}
\displaystyle \\
\displaystyle \textbf{Simple Interest}
\displaystyle \text{Simple interest is interest calculated only on the original principal}
\displaystyle \text{throughout the entire period of the loan or investment.}
\displaystyle \text{It is denoted by S.I.}
\displaystyle \text{The interest for each equal time period remains the same when the}
\displaystyle \text{principal and the rate of interest remain unchanged.}
\displaystyle \text{No interest is calculated on the interest already earned or charged.}
\displaystyle \\
\displaystyle \textbf{Formula for Simple Interest}
\displaystyle \text{Let }P=\text{Principal, }R=\text{Rate per annum and }T=\text{Time in years}.
\displaystyle \text{Then,}
\displaystyle \text{S.I.}=\frac{P\times R\times T}{100}.
\displaystyle \\
\displaystyle \textbf{Finding the Principal}
\displaystyle P=\frac{100\times\text{S.I.}}{R\times T}.
\displaystyle \\
\displaystyle \textbf{Finding the Rate of Interest}
\displaystyle R=\frac{100\times\text{S.I.}}{P\times T}.
\displaystyle \\
\displaystyle \textbf{Finding the Time}
\displaystyle T=\frac{100\times\text{S.I.}}{P\times R}.
\displaystyle \\
\displaystyle \textbf{Amount under Simple Interest}
\displaystyle \text{Amount}=\text{Principal}+\text{Simple Interest}.
\displaystyle A=P+\frac{P\times R\times T}{100}.
\displaystyle A=P\left(1+\frac{RT}{100}\right).
\displaystyle \\
\displaystyle \textbf{Important Notes on Time}
\displaystyle \text{If time is given in months, convert it into years before using a rate}
\displaystyle \text{given per annum. Thus, }T=\frac{\text{Number of months}}{12}.
\displaystyle \text{If time is given in days, the convention stated in the question or}
\displaystyle \text{textbook should be followed when converting days into years.}
\displaystyle \text{For exact simple interest, }T=\frac{\text{Number of days}}{365}\text{ is commonly used}.
\displaystyle \text{When counting the number of days between two dates, the usual convention}
\displaystyle \text{is to exclude the first day and include the last day.}
\displaystyle \\
\displaystyle \textbf{Compound Interest}
\displaystyle \text{Compound interest is interest calculated on the principal as well as on}
\displaystyle \text{the interest accumulated during the previous compounding periods.}
\displaystyle \text{Thus, after each compounding period, the interest is added to the}
\displaystyle \text{principal and the resulting amount becomes the new principal.}
\displaystyle \text{Compound interest is abbreviated as C.I.}
\displaystyle \\
\displaystyle \textbf{Amount under Compound Interest}
\displaystyle \text{If interest is compounded annually at }R\%\text{ p.a. for }T\text{ years,}
\displaystyle A=P\left(1+\frac{R}{100}\right)^T.
\displaystyle \\
\displaystyle \textbf{Compound Interest Formula}
\displaystyle \text{C.I.}=\text{Amount}-\text{Principal}.
\displaystyle \text{C.I.}=A-P.
\displaystyle \text{Therefore, C.I.} =P\left[\left(1+\frac{R}{100}\right)^T-1\right].
\displaystyle \\
\displaystyle \textbf{Simple Interest versus Compound Interest}
\displaystyle \text{In simple interest, interest is calculated only on the original principal.}
\displaystyle \text{In compound interest, interest is calculated on the principal as well as}
\displaystyle \text{on the interest accumulated during earlier compounding periods.}
\displaystyle \text{Therefore, for the same principal, positive rate and time, compound}
\displaystyle \text{interest generally exceeds simple interest when compounding occurs over}
\displaystyle \text{more than one compounding period.}
\displaystyle \\

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