Working out profit, discounts and interest on money
Profit and loss compare the selling price (SP) with the cost price (CP). Profit = SP − CP, and profit percentage is always calculated on the cost price: (profit ÷ CP) × 100. A shop that buys a bag for ₹800 and sells it for ₹1000 makes a profit of ₹200, which is 25%. Discount is different, because it is taken off the marked price: a 20% discount on a marked price of ₹1500 gives a selling price of ₹1200. Two successive discounts of 20% and 10% amount to 28%, not 30%, because the second applies to the already reduced price.
Simple interest is charged only on the original principal: SI = P × R × T ÷ 100. Compound interest adds each year's interest to the principal, so the next year's interest is charged on a larger amount. The amount after n years is A = P(1 + R/100)ⁿ, and the compound interest is A − P. On ₹10,000 at 10% for two years, simple interest is ₹2,000 but compound interest is ₹2,100. For half-yearly compounding, halve the rate and double the number of periods.
Why it matters
These calculations are used every day in shopping, running a business, bank deposits, loans and EMIs. Understanding compound interest shows why starting to save early helps and why unpaid credit card balances grow quickly. GST, commission and depreciation questions use the same percentage ideas, and the compound interest formula is a geometric progression that you meet again in Class 11.
Key terms
- Cost price
- The amount paid to buy or make an item, on which profit and loss percentages are based.
- Marked price
- The price printed on an item before any discount is taken off.
- Principal
- The original sum of money that is lent, borrowed or deposited.
- Compound interest
- Interest calculated on the principal plus all interest already added.