Profit, Loss, and Interest

Lesson 4 of 4: Topic 5 Fractions

In this lesson:

• Calculate profit or loss, and the percentage profit or loss
• Use the formula for simple interest
• Solve reverse and combined financial problems

What You Will Learn Today

By the end of this lesson:

1. Calculate profit or loss (CP and SP given)
2. Calculate percentage profit or loss on CP
3. Find SP from CP and a profit/loss percentage
4. Use and find the amount
5. Solve multi-skill real-life financial problems

Two Moves You Already Own

Two moves from fractions-03 power every calculation today:

• Move 1 — Percentage of a quantity: 15% of 2,000 = ?
• Move 2 — Express as a percentage: 12 out of 40 = ?

Quick recall — answer both before the next slide.

The Radio: Where Does the Money Go?

Amina buys a radio for 5,000 sh (cost price) and sells it for 6,500 sh (selling price).

• Which price is bigger?
• Subtract to find the gap.

What do we call that gap? That's today's first idea.

Always Compare Prices First, Then Subtract

• CP: what you pay · SP: what you receive
• Compare first — subtract for the positive gap:
  • SP > CP → Profit = SP − CP
  • CP > SP → Loss = CP − SP

Radio: SP 6,500 > CP 5,000 → Profit = 1,500 sh

Profit or Loss? You Decide

Amina's neighbour buys the same radio for 5,000 sh and sells it for 4,200 sh.

• Which price is bigger: 5,000 or 4,200?
• Is this a profit or a loss?
• Calculate the amount.

Moving to "Per 100 Invested"

We know Amina made 1,500 sh profit on a 5,000 sh radio.

A new question: for every 100 shillings she invested, how many did she gain?

That is the percentage profit — and it is the fractions-03 "express one quantity as a percentage of another" move applied to money.

Percentage Profit and Loss on Cost Price

The cost price is always the whole — it is what was invested.

Profit = the part. Cost price = the whole. Always.

Worked: Percentage Profit and Loss

Profit case: Profit = 1,500 sh, CP = 5,000 sh

Loss case: Loss = 800 sh, CP = 5,000 sh

Which Base Is the Right One?

Discount vs Profit — Different Bases

Different problems, different bases. Do not carry the profit rule into a discount problem.

Quick Check: Find the Percentage Profit

A trader buys cloth for 12,000 sh and sells it for 15,000 sh.

1. What is the profit in shillings?
2. What is the percentage profit?

Work it out, then check your base — did you divide by 12,000 or 15,000?

A New Money Problem: Saving and Borrowing

So far: profit and loss measure how money changes through trade.

Now: interest measures how money grows over time through saving or borrowing.

Same underlying idea — measuring a change relative to a starting amount — but a different formula for a different situation.

Three Quantities Before the Formula

Simple interest depends on three things:

• P — Principal: the money saved or borrowed (starting amount)
• R — Rate: the percentage per year (annual interest rate)
• T — Time: the number of years (not months)

Name all three before you substitute anything.

The Formula: I = PRT ÷ 100

• R = plain percentage number (enter 10, not 0.10)
• ÷100 converts R once — do not also write 0.10
• T in years — convert months first (6 months = 0.5 yr)
• Amount =

Worked: Simple Interest and Amount

P = 100,000 · R = 10% · T = 2 yr

Interest:

Amount:

Time-unit: 6 months = 0.5 yr → substitute 0.5

Spot the Mistake in This Working

A student calculated:

Two questions:

• What went wrong?
• How large should the answer be?

A size check: 10% of 100,000 for one year = 10,000 sh, so two years = 20,000 sh. Does 200 make sense?

Quick Check: Interest and Amount

Nakato saves 80,000 sh at 12% per year for 3 years.

1. Identify P, R, and T
2. Calculate the interest I
3. Calculate the total amount

Remember: R = 12 (not 0.12), T = 3 years.

Now Run the Same Skills Backwards

We can now find profit, loss, and interest. Chunk 4 runs these skills backwards:

• Given CP and % profit → find SP
• Given I, P, R → find T
• One combined problem drawing on the whole topic

The same skills, run in a different direction.

Find SP from a Target Profit Percentage

CP = 8,000 sh, profit target = 25%

Step 1 — Profit amount:

Step 2 — SP:

Loss (10%): SP = 8,000 − 800 = 7,200 sh

Reverse the Formula to Find Time

Given: I = 15,000 sh, P = 50,000 sh, R = 10%. Find T.

Substitute what you know:

Simplify and solve for T:

Your Turn: The Rice Problem

A trader buys 40 kg of rice at 2,000 sh per kg.
She sells 3/4 of it at a 20% profit and the rest at cost price.

Find the total money she receives from the sale.

One Move Powers All Three Situations

• SP > CP = profit; CP > SP = loss (compare first)
• % profit/loss base = CP, not SP
• I = PRT ÷ 100: R = plain number; T in years
• Amount = P + I (not just I)

Next: compound interest, hire purchase, VAT.