Key Concepts

Habari Mwanafunzi! Welcome to Business Mathematics!

Have you ever bought a smokie or a samosa during break time and wondered how the person selling it makes money? Or maybe you've seen a big "SALE!" sign in a shop and wanted to know exactly how much you're saving. Well, you've come to the right place! Today, we are diving into the Key Concepts of Business Mathematics. Think of these as the secret codes that unlock the world of money, business, and making smart financial decisions. Let's get started!

1. Profit and Loss: The Heartbeat of Business

Every business, from the lady selling sukuma wiki at the market to big companies like Safaricom, is interested in one main thing: making a profit. But sometimes, things don't go as planned, and they might make a loss.

• Cost Price (CP): This is the amount of money you spend to buy or create a product. Let's call it the 'buying price'.
• Selling Price (SP): This is the price at which you sell the product to a customer.

The rule is simple:

• If the Selling Price is more than the Cost Price, you have made a PROFIT (Pesa imeongezeka!).
• If the Selling Price is less than the Cost Price, you have made a LOSS (Hapo umepoteza pesa kidogo).

Example Scenario:

Amina, a student, decides to start a small hustle. She goes to Gikomba market and buys 10 t-shirts for KES 150 each. This is her Cost Price. She then sells each t-shirt to her friends in school for KES 250. This is her Selling Price.

Let's calculate Amina's profit for one t-shirt:

Formula: Profit = Selling Price (SP) - Cost Price (CP)

Step 1: Identify the SP and CP.
   SP = KES 250
   CP = KES 150

Step 2: Apply the formula.
   Profit = 250 - 150
   Profit = KES 100

Amina makes a profit of KES 100 on every t-shirt she sells!

Here's a simple way to visualize it:

      PROFIT (+)                 LOSS (-)
        / \                       / \
       /   \                     /   \
  Selling > Cost             Cost > Selling
   Price     Price           Price    Price

   (KES 250 > KES 150)       (KES 150 > KES 120)
       = You Win!              = You Lose!

Image Suggestion:

A vibrant, colourful Gikomba market scene in Nairobi. A young, determined teenage girl (like Amina) is smiling as she negotiates with a friendly vendor over a stack of cool, modern t-shirts. The style should be a bright, realistic digital painting.

2. Discounts: Everyone Loves a Good Deal!

You see this everywhere - "Black Friday Sale!", "Toi Market Clearance!", "50% Off!". A discount is a reduction in the normal price of an item. It's a way for businesses to attract more customers.

• Marked Price (MP): The original price tag on the item before any sale.
• Discount: The amount of money taken off the Marked Price. It's usually given as a percentage (%).

Example Scenario:

You want to buy new sports shoes from Bata. The price tag (Marked Price) says KES 3,000. But there is a sign that says "20% OFF FOR STUDENTS!". Let's find out your final price.

Here's how to calculate the new selling price:

Step 1: Calculate the Discount Amount.
   Formula: Discount Amount = Discount % of Marked Price
   
   Discount Amount = 20% of 3000
   Discount Amount = (20 / 100) * 3000
   Discount Amount = 0.2 * 3000
   Discount Amount = KES 600
   (So, you are saving KES 600!)

Step 2: Calculate the Final Selling Price.
   Formula: Selling Price = Marked Price - Discount Amount

   Selling Price = 3000 - 600
   Selling Price = KES 2,400

You will pay only KES 2,400 for those cool shoes!

Think of it like a price tag being changed:

+-------------------------+
|      BATA SPORTS SHOES      |
|                         |
|   Original Price:       |
|      ~KES 3,000~        |
|                         |
|   20% DISCOUNT!         |
|                         |
|   NOW ONLY: KES 2,400   |
|                         |
+-------------------------+

3. Simple Interest: Let Your Money Work for You!

Instead of keeping your money under a mattress, you can put it in a bank or a SACCO and earn extra money called interest. On the other hand, if you borrow money (take a loan), you have to pay back the original amount plus an extra fee, which is also interest.

• Principal (P): The initial amount of money you save or borrow.
• Rate (R): The percentage at which interest is calculated per year.
• Time (T): The duration for which the money is borrowed or saved, usually in years.

Example Scenario:

Your uncle gives you KES 5,000 as a gift. You decide to be smart and deposit it into a local Youth SACCO account that offers a simple interest rate of 8% per year. You want to see how much money you will have after 2 years.

Let's calculate the Simple Interest and the final amount:

Step 1: Calculate the Simple Interest (I).
   Formula: I = P * R * T

   Principal (P) = 5000
   Rate (R) = 8% = 8/100 = 0.08
   Time (T) = 2 years

   I = 5000 * 0.08 * 2
   I = 400 * 2
   I = KES 800

   In 2 years, your money has earned you an extra KES 800, just by sitting there!

Step 2: Calculate the Total Amount (A) in your account.
   Formula: Amount = Principal + Interest

   A = 5000 + 800
   A = KES 5,800

After 2 years, your account will have KES 5,800!

Image Suggestion:

An illustration of a Kenyan student proudly holding a SACCO passbook. In the background, a money plant is growing from a pot, with glowing coins hanging from its leaves, symbolizing the growth of savings through interest. The style is optimistic and slightly stylized.

Tusonge Mbele! (Let's Move Forward!)

Congratulations! You have just learned the fundamental language of business. Understanding Profit & Loss, Discounts, and Simple Interest is like having a superpower. It helps you understand how shops work, how to save your money wisely, and how to spot a great deal.

Keep practicing, stay curious, and you'll be a business math guru in no time. You've got this!