Commercial Arithmetic (I)
Numbers · Commercial Arithmetic (I)
Syllabus tag: KCSE | Mathematics | Form 1 | Topic 18 Commercial Arithmetic (I)
Lesson objectives
By the end of this topic, you should be able to:
- Convert currency from one form into another given the exchange rates.
- Calculate profit and loss.
- Express profit and loss as percentages.
- Calculate discount, commission and simple interest.
Commercial Arithmetic (I)
This topic applies percentages to trade, banking and borrowing.
a) Currency conversion
Banks quote two rates for each currency.
The buying rate is what the bank pays when it buys foreign currency from you.
The selling rate is what the bank charges when it sells foreign currency to you.
The selling rate is always higher. The difference is the bank's profit.
Work out which side you are on before choosing a rate. If you arrive with dollars and want shillings, the bank is buying, so use the buying rate.
Choosing the wrong rate is the standard error in this topic.
b) Profit and loss
Profit = selling price − buying price.
Loss = buying price − selling price.
For the percentage, always divide by the buying price, not the selling price.
The buying price is what was invested, so it is what the gain is measured against.
c) Discount
A discount is a reduction from the marked price.
Work out the percentage of the marked price, then subtract.
A shortcut: 15% off means you pay 85%, so multiply the marked price by 0.85.
Marked price is the label price. Selling price is what is actually paid after discount.
d) Commission
Commission is payment for selling, worked out as a percentage of the value sold.
An agent on 5% commission who sells goods worth KES 400 000 earns KES 20 000.
Some agents receive a basic salary plus commission. Add the two for total earnings.
e) Simple interest
Simple interest is calculated on the original principal for the whole period.
The formula is I = PRT/100. Here P is the principal, R the rate per year, and T the time in years.
The amount is the principal plus the interest.
Keep T in years. Nine months is 0.75 years, not 9.
f) Rearranging the formula
Any one of the four can be found if the other three are known.
P = 100I/RT. R = 100I/PT. T = 100I/PR.
g) Where this is used
Changing money for travel. Pricing goods for a shop. Judging a loan offer. Working out what a salesperson earns.
Words to know
- Cost price -- the price at which goods are bought.
- Marked price -- the advertised price before any discount.
- Discount -- a reduction from the marked price.
- Commission -- a payment to an agent, usually a percentage of sales.
- Principal -- the sum of money invested or borrowed.
:::checkpoint Check yourself
- A bank buys USD at KES 128 and sells at KES 132. How many shillings do you get for USD 200?
- An item bought for KES 1 500 sells for KES 1 800. Find the percentage profit.
- Find the simple interest on KES 50 000 at 6% for 4 years.
- Why is percentage profit calculated on the buying price? :::
Bridge to practice
The exercises begin with profit, loss and their percentages, move through discount, commission and simple interest, and finish with currency conversion. For each question, write down what the percentage is a percentage of before doing any arithmetic.