Learning Objectives
- Understand and calculate ratios and percentages
- Find increase or decrease percent
- Calculate simple and compound interest
- Apply concepts of discount, profit, loss, and sales tax/VAT
Key Concepts
Ratios and Percentages
A ratio compares two quantities of the same kind. Percentage means "per hundred." To convert a fraction to percentage: multiply by 100. To convert percentage to fraction: divide by 100.
Increase %: (Increase / Original Value) × 100
Decrease %: (Decrease / Original Value) × 100
Profit and Loss
Profit: Selling Price (SP) - Cost Price (CP), when SP > CP.
Loss: CP - SP, when CP > SP.
Profit %: (Profit / CP) × 100
Loss %: (Loss / CP) × 100
Discount
Marked Price (MP): The price printed on the article (also called list price).
Discount: Reduction given on the marked price. Discount = MP - SP.
Discount %: (Discount / MP) × 100
Sales Tax and VAT
Sales tax is charged by the government on the sale of goods. It is added to the bill amount.
Bill Amount: SP + Sales Tax
Compound Interest
In compound interest, interest is calculated on the principal plus accumulated interest.
Formula: A = P(1 + R/100)ⁿ, where A = Amount, P = Principal, R = Rate per annum, n = Number of years.
Compound Interest (CI): CI = A - P
Simple Interest: SI = (P × R × T) / 100
Compound interest is always greater than or equal to simple interest for the same principal, rate, and time (when n ≥ 2).
Applications of Compound Interest
The compound interest formula is used in population growth, depreciation of value, and bacterial growth. For depreciation: A = P(1 - R/100)ⁿ.
Summary
Comparing quantities involves ratios, percentages, profit and loss, discount, tax, and interest calculations. Simple interest is calculated on the original principal only, while compound interest is calculated on the principal plus accumulated interest. The compound interest formula has applications in population growth and depreciation.
Important Terms
- Cost Price (CP): The price at which an article is purchased
- Selling Price (SP): The price at which an article is sold
- Marked Price (MP): The printed/listed price of an article
- Discount: Reduction on the marked price
- Compound Interest: Interest calculated on principal plus accumulated interest
- Depreciation: Decrease in value over time
Quick Revision
- Profit % = (Profit / CP) × 100; Loss % = (Loss / CP) × 100
- Discount = MP - SP; Discount % = (Discount / MP) × 100
- SI = PRT/100
- CI formula: A = P(1 + R/100)ⁿ; CI = A - P
- Depreciation: A = P(1 - R/100)ⁿ
- Compound interest ≥ simple interest for same P, R, and n ≥ 2