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Number - Financial Mathematics: Profit, Loss, Simple Interest

Grade 7IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Cost Price (CP) and Selling Price (SP): The Cost Price is the total amount paid to purchase a good or service, including any overhead expenses. The Selling Price is the amount at which the good is sold to a customer. Visualize this as a financial flow: money moving into a business (CP) versus money flowing back to the business from a sale (SP).

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Profit and Loss: Profit occurs when the selling price is higher than the cost price (SP>CPSP > CP), while a Loss occurs when the cost price is higher than the selling price (CP>SPCP > SP). Imagine a vertical bar chart where the difference in height between the CP and SP bars represents either the 'surplus' (profit) or the 'gap' (loss).

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Profit and Loss Percentage: These values express the gain or loss relative to the original Cost Price, allowing for easier comparison between different investments. To visualize this, think of the Cost Price as a full 100100\\% bar; a profit percentage is an additional segment extending beyond that 100100\\% mark, whereas a loss percentage is a missing segment within that bar.

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Simple Interest (SI): This is the interest calculated only on the initial amount of money borrowed or invested, known as the Principal. Unlike compound interest, simple interest does not grow on top of previous interest. Visualize a timeline where the investment grows by a fixed, identical amount of money every single year.

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Principal, Rate, and Time: The Principal (PP) is the initial sum, the Rate (RR) is the annual percentage of interest, and Time (TT) is the duration in years. You can visualize the Principal as a 'seed' and the Rate as the 'growth speed'. The more Time that passes, the more 'fruit' (interest) the seed produces.

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Total Amount: The Amount (AA) is the final value of an investment or loan after the simple interest has been added back to the Principal. On a graph, this is represented by the total height of a stacked bar where the bottom section is the Principal and the top section is the accumulated Interest.

📐Formulae

Profit=SP−CPProfit = SP - CP

Loss=CP−SPLoss = CP - SP

ProfitProfit \\% = (\\frac{Profit}{CP}) \\times 100

LossLoss \\% = (\\frac{Loss}{CP}) \\times 100

I=fracPtimesRtimesT100I = \\frac{P \\times R \\times T}{100}

A=P+IA = P + I

💡Examples

Problem 1:

A retailer buys a smartphone for 400andsellsitforand sells it for 460460. Calculate the profit made and the profit percentage.

Solution:

  1. Identify the given values: CP=400CP = 400 and SP=460SP = 460.
  2. Calculate the Profit: Profit=SP−CP=460−400=60Profit = SP - CP = 460 - 400 = 60.
  3. Use the Profit percentage formula: ProfitProfit \\% = (\\frac{Profit}{CP}) \\times 100.
  4. Substitute the values: ProfitProfit \\% = (\\frac{60}{400}) \\times 100.
  5. Simplify: ProfitProfit \\% = 0.15 \\times 100 = 15\\%.

Explanation:

First, we find the absolute profit by subtracting the cost price from the selling price. Then, we find what percentage that profit is of the original cost price (CPCP).

Problem 2:

Find the simple interest and the total amount to be paid back on a loan of 2500ataninterestrateofat an interest rate of8\%peryearforper year for4$ years.

Solution:

  1. Identify the given values: P=2500P = 2500, R=8R = 8, and T=4T = 4.
  2. Use the Simple Interest formula: I=fracPtimesRtimesT100I = \\frac{P \\times R \\times T}{100}.
  3. Substitute the values: I=frac2500times8times4100I = \\frac{2500 \\times 8 \\times 4}{100}.
  4. Calculate the Interest: I=25times32=800I = 25 \\times 32 = 800.
  5. Calculate the Total Amount: A=P+I=2500+800=3300A = P + I = 2500 + 800 = 3300.

Explanation:

Simple interest is calculated by multiplying the principal, rate, and time together and then dividing by 100. The total amount is the sum of the original loan and the interest earned.