EQN-01-10

Profit, Loss & Simple Interest

Compute profit/loss percentages on cost price and simple interest with one clean formula each.

~5 min read•Difficulty 2/5

Profit and loss are percentages of the COST

profit = selling price - cost price

profit % = profit / cost price \times 100

The base is always the cost price, not the selling price. A loss uses the same formula with a negative profit.

Selling price from a profit percent

selling price = cost \times (1 + profit %/100)

Cost 200 at 15% profit $\to 200 \times 1.15 = 230.$

Simple interest

interest = principal \times rate \times time (rate as a decimal, time in years)

I = P \cdot r \cdot t

Total amount owed/saved $=$ principal $+$ interest.

1000 at 5% for 3 years \to I = 1000 \times 0.05 \times 3 = 150 \to total 1150.

Simple vs compound

Simple interest is charged only on the original principal each year. Compound interest is charged on the growing balance — on the GAT-E, assume simple unless "compound" is stated.

Worked examples

Example 1 (difficulty 2/5)

An item costing 80 is sold for 100. What is the profit percent?

◎ Predict the answer first:

Example 2 (difficulty 2/5)

Find the simple interest on 2000 at 4% per year for 3 years.

◎ Predict the answer first:

Tips

Profit/loss percent always uses the COST price as the base.
Selling price $=$ cost $\times (1 \pm$ profit/loss rate).
Simple interest $I =$ Prt — convert the rate to a decimal and the time to years.

Common mistakes

Dividing profit by the selling price

Why: The selling price is the bigger, more visible number.

Fix: The base for profit percent is the cost price.

Reporting the total amount when only the interest is asked

Why:

P + I

feels like "the answer".

Fix: Read carefully: interest is just Prt; add P only if the total is requested.

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