# Percentage Basis Concept

**A percentage is a way of expressing a number as a fraction of 100 (per cent meaning “per hundred”). It is often denoted using the percent sign, “%”, or the abbreviation “pct”. Since a percent is an amount per 100, percent can be represented as fractions with a denominator of 100. For example, 25% means 25 per 100, 25/100 and 350% means 350 per 100, 350/100.**

**• A percent can be represented as a decimal. The following relationship characterizes how percent and decimals interact. Percent Form / 100 = Decimal Form **

**For example: What is 2% represented as a decimal? Percent Form / 100 = Decimal Form: 2%/100=0.02 **

**Percent change**

**The general formula for percent increase or decrease, (percent change):**

**[latex] percent=\frac{change}{original}*100 [/latex]**

**Example:** **A company received Rs2 million in royalties on the first Rs10 million in sales and then Rs8 million in royalties on the next Rs100 million in sales. By what percent did the ratio of royalties to sales decrease from the first Rs10 million in sales to the next Rs100 million in sales?**

**Solution**: Percent decrease can be calculated by the formula above:

**we know the general formula:**

**[latex] percent=\frac{change}{original}*100 [/latex]**

**[latex] = \frac{\frac{2}{10}-\frac{8}{10}}{\frac{2}{10}}*100\, = 60% [/latex]**

**Simple Interest ****Simple interest = principal * interest rate * time, where “principal” is the starting amount and “rate” is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate.**

**Example: If Rs15,000 is invested at 10% simple annual interest, how much interest is earned after 9 months?**

**Solution:** **Rs15,000*0.1*9/12 = Rs1125 **

**Compound Interest**

**The interest will be added to the initial principal after every compounding period. Hence, the compound interest keeps on increasing after every .compounding period. **