Money
Interactive curriculum lessons, worked examples, and geometric problem-solving techniques designed to help Kenyan students master CBC, KPSEA, KCSE, and IGCSE mathematics.
First Principles
Objective: Understand and calculate simple interest on loans or savings, and commission on sales transactions.
Concrete Scenario: Mama Wanjiku joins a local chama (table-banking group). She borrows KSh 10,000 at a rate of 10% simple interest per year to expand her vegetable stall. If she repays after 3 years, how much extra money (interest) does she pay back?
Geometric & Visual Insight: Picture simple interest as identical blocks of interest added at the end of each year.
• In Year 1, she pays \(10\%\) of KSh 10,000 = KSh 1,000.
• In Year 2, the interest slice is identical: KSh 1,000.
• In Year 3, another identical slice: KSh 1,000.
Unlike compound interest, the principal never changes; the interest slices remain constant: \[\text{Total Interest} = \text{One Year's Interest} \times \text{Number of Years}\]
What is Commission? Commission works under the exact same percentage principle. A sales agent earns a percentage slice of the total value of goods sold: \[\text{Commission} = \frac{R}{100} \times \text{Value of Sales}\]
Interactive Interest & Commission Explorer
Adjust Principal \(P\), Rate \(R\), and Time \(T\) to visualize annual interest slices.
Key Formulas
1. Simple Interest:
\[I = \frac{P \times R \times T}{100}\]Where:
• \(P\) = Principal (original amount borrowed or invested in KSh)
• \(R\) = Annual rate of interest (in % per annum)
• \(T\) = Time period (in years)
2. Total Amount Accumulated / Repayable:
\[A = P + I = P\left(1 + \frac{R \times T}{100}\right)\]3. Time in Months Conversion:
If time \(m\) is given in months, convert to years:
\[T = \frac{m}{12} \implies I = \frac{P \times R \times m}{100 \times 12}\]4. Sales Commission & Gross Earnings:
\[\text{Commission} = \frac{\text{Commission Rate}}{100} \times \text{Total Sales}\] \[\text{Gross Earnings} = \text{Basic Salary} + \text{Commission}\]Worked Examples
Example 1 (Easy): Basic Commission Calculation
Amina sells solar lamps in Eldoret. She earns a \(6\%\) commission on all sales. If she sells lamps worth KSh 45,000 in one month, how much commission does she receive?
- Identify the knowns: Total Sales = KSh 45,000, Commission Rate = \(6\%\).
- Apply the formula: \[\text{Commission} = \frac{6}{100} \times 45\,000\]
- Simplify: \[\text{Commission} = 6 \times 450 = 2\,700\]
Answer: KSh 2,700
Example 2 (Medium): Simple Interest with Time in Months
Otieno borrows KSh 24,000 from a SACCO at a simple interest rate of \(15\%\) per annum for \(8\) months. Calculate the total amount he must repay.
- Identify the knowns: \(P = 24\,000\), \(R = 15\%\), \(T = \frac{8}{12} = \frac{2}{3}\) years.
- Calculate Simple Interest: \[I = \frac{P \times R \times T}{100} = \frac{24\,000 \times 15 \times \frac{2}{3}}{100}\] \[I = 240 \times 15 \times \frac{2}{3} = 240 \times 10 = 2\,400\]
- Calculate Total Amount to Repay: \[A = P + I = 24\,000 + 2\,400 = 26\,400\]
Answer: KSh 26,400
Example 3 (Hard): Tiered Commission and Net Profit
A real estate broker in Nakuru is paid a basic monthly salary of KSh 30,000 plus \(3\%\) commission on any property sales above KSh 500,000. In December, he sells a plot of land for KSh 1,800,000. How much are his total earnings for December?
- Find sales eligible for commission: \[\text{Eligible Sales} = 1\,800\,000 - 500\,000 = 1\,300\,000\]
- Calculate commission earned: \[\text{Commission} = \frac{3}{100} \times 1\,300\,000 = 3 \times 13\,000 = 39\,000\]
- Add basic salary to get total earnings: \[\text{Total Earnings} = 30\,000 + 39\,000 = 69\,000\]
Answer: KSh 69,000
Common Mistakes
Real World
1. Chama Table Banking & Micro-Loans:
Across East Africa, women and youth groups run table-banking chamas. Members take emergency or business development loans at simple interest (e.g., \(10\%\) per year). If a member borrows KSh 15,000 to buy stock for 6 months, the interest charged is \(15\,000 \times 0.10 \times 0.5 = \text{KSh } 750\), making repayment manageable and transparent.
2. Agricultural Commodity & Livestock Agents:
In rural markets like Kitale or Nyahururu, commission brokers connect farmers to wholesale buyers. If a broker negotiates the sale of 100 bags of potatoes at KSh 2,500 each (total KSh 250,000) at a \(4\%\) commission rate, the broker earns \(250\,000 \times 0.04 = \text{KSh } 10\,000\).
3. Hire Purchase & Retail Financing:
Electronics and motorbikes (boda bodas) are frequently bought on hire purchase. The finance company adds simple interest to the cash price, and the customer repays the total amount \(A = P + I\) in equal monthly installments.
Practice