Introduction to various terms used in Simple Interest and Compound Interest:

Principal: This is the money borrowed or lent out for a certain period of time is called the principal or sum.

Interest: Interest is payment from a borrower to a lender of an amount above repayment of the principal sum

Amount: The total money paid back by the borrower to the lender is called the amount.

$\displaystyle \text{Amount = Principal + Interest}$

Rate: The interest on Rs. 100 for a unit time is called the rate of interest. It is expressed in %. The interest on Rs. 100 for 1 year is called rate % per annum (abbreviated as rate % p. a.)

Simple Interest

• Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains. It excludes the effect of compounding. It is denoted by S.I.
• The simple interest is calculated uniformly only on the original principal throughout the loan period.
• You do not earn interest on the interest earned during the loan period.

Formulas$\displaystyle \text{Let Principal = P, Rate = R\% per annum and Time T years. Then, we have:}$

$\displaystyle \text{i) } S.I. = \frac{P \times R \times T}{100}$

$\displaystyle \text{ii) } P = \frac{100 \times S.I}{R \times T}$

$\displaystyle \text{iii) } R = \frac{100 \times S.I}{P \times T}$

$\displaystyle \text{iv) } T = \frac{100 \times S.I}{P \times R}$

Notes:

• While calculating the time period between two given dates, the day on which the money is borrowed is not counted for interest calculations while the day on which the money is returned, is counted for interest calculations.
• For converting the time in days into years, we always divide by 365, whether it is an ordinary year or a leap year.

Compound Interest

• Compound interest includes interest earned on the interest which was previously accumulated.
• Here you also earn interest over the interest accrued during the loan period.
• The difference between the final amount and the original principal is called the compound interest (abbreviated as C.I.)

$\displaystyle \text{Compound Interest (C.I.) = Final Amount - Original Principal}$