Learning Objectives
  • Calculate profit, loss, discount and percentage change.
  • Use simple and compound interest formulas.
  • Solve appreciation and depreciation problems.
  • Perform currency conversions using stated exchange rates.
  • Interpret bills, instalments and financial information accurately.
Key Terms
Cost price
The amount paid to obtain an item.
Selling price
The amount received when an item is sold.
Profit
Selling price minus cost price.
Loss
Cost price minus selling price.
Simple interest
Interest calculated only on the original principal.
Compound interest
Interest calculated on the current balance, including previous interest.
Depreciation
A repeated percentage decrease in value.
Exchange rate
A rule for converting one currency to another.
8th Edition Chapter Map
  • Profit, loss, markup and discount
  • Simple interest
  • Compound interest and depreciation
  • Currency conversion
  • Bills, instalments and reverse percentage
Profit And Loss
\text{profit}=\text{selling price}-\text{cost price}
\text{profit percentage}=\frac{\text{profit}}{\text{cost price}}\times100\%

Profit or loss percentages are normally calculated as a percentage of the cost price unless the question states otherwise. A markup is an increase from cost price to selling price.

Worked Example: Profit Percentage

Question: A trader buys a device for 48 000 and sells it for 57 600. Find the profit percentage.

  1. Profit =57600-48000=9600.
  2. Percentage =9600/48000\times100=20\%.

Answer: The profit percentage is 20\%.

Discount

A discount is a percentage reduction from the marked price. Calculate the discount amount or multiply directly by the remaining percentage.

Worked Example: Successive Discounts

Question: An item marked 8 000 is reduced by 15%, then by a further 10%. Find the final price.

  1. After 15% discount: 8000\times0.85=6800.
  2. After another 10%: 6800\times0.90=6120.
  3. The combined discount is not 25%; it is applied to changing amounts.

Answer: The final price is 6 120.

Simple Interest

Simple interest is based only on the original principal. If P is the principal, r the annual percentage rate and t the time in years, then:

I=\frac{Prt}{100}
Worked Example: Simple Interest

Question: Find the total after 3.5 years when 60 000 is invested at 8% simple interest per year.

  1. I=60000\times8\times3.5/100=16800.
  2. Total =60000+16800=76800.

Answer: The total is 76 800.

Compound Interest

Compound growth uses the current balance each period. Convert the percentage rate to a multiplier. An increase of r\% uses 1+r/100.

A=P\left(1+\frac{r}{100}\right)^n
Worked Example: Compound Interest

Question: 20 000 is invested at 6% compound interest for 4 years. Find the value.

  1. Growth multiplier =1.06.
  2. A=20000(1.06)^4.
  3. A\approx25249.54.

Answer: Approximately 25 250, to the nearest unit.

Depreciation

A decrease of r\% uses multiplier 1-r/100. Repeated depreciation is exponential decay, not repeated subtraction of a fixed amount.

Worked Example: Depreciation

Question: A car worth 4 500 000 depreciates by 12% each year. Find its value after 3 years.

  1. Decay multiplier =0.88.
  2. V=4500000(0.88)^3.
  3. V=3066624.

Answer: The value is 3 066 624.

Reverse Percentage

When the final amount is known, divide by the multiplier to recover the original. Do not subtract the percentage from the final amount.

Worked Example: Original Price

Question: After a 20% discount, a jacket costs 7 200. Find the marked price.

  1. The sale price is 80% of the marked price.
  2. 0.8M=7200.
  3. M=7200/0.8=9000.

Answer: The marked price was 9 000.

Currency Conversion

Read the direction of the exchange rate. If 1 USD = 280 PKR, multiply dollars by 280 to obtain rupees and divide rupees by 280 to obtain dollars. Commission or service charges must be handled separately.

Worked Example: Exchange And Commission

Question: A traveller changes 150 000 PKR into dollars at 1 USD = 278 PKR. The exchange service charges 1.5% of the rupee amount. Find the dollars received.

  1. Commission =150000\times0.015=2250 PKR.
  2. Amount exchanged =147750 PKR.
  3. Dollars =147750/278\approx531.47.

Answer: Approximately USD 531.47.

Bills And Instalments

Financial questions may include standing charges, unit charges, taxes or instalment deposits. Organise the calculation in stages and check whether a percentage applies before or after a fixed charge.

Situation Useful model
Fixed charge plus unit cost C=mn+c
One percentage increase Multiply by 1+r/100
One percentage decrease Multiply by 1-r/100
Repeated percentage change Use a power of the multiplier
Recover original amount Divide by the multiplier
Examination Guidance
  • Keep full calculator values during compound-interest work and round only at the end.
  • Write the percentage multiplier before calculating.
  • Check the base quantity for profit, loss and discount percentages.
  • For currency, label each amount with its currency throughout.
Common Mistakes
  • Adding percentage rates for successive discounts.
  • Using simple interest when the balance changes each year.
  • Subtracting a percentage from the final price in reverse-percentage questions.
  • Multiplying when the exchange-rate direction requires division.
Knowledge Check And Practice

1. An item costing 5 000 is sold for 5 750. Find the profit percentage.

Answer: Profit =750; percentage =750/5000\times100=15\%.

2. Find the simple interest on 24 000 at 7.5% for 2 years.

Answer: 3600.

3. 12 000 grows by 4% annually for 3 years. Find the amount.

Answer: 12000(1.04)^3\approx13498.37.

4. A value falls by 18%. State the multiplier.

Answer: 0.82.

5. After a 25% increase, a salary is 75 000. Find the original salary.

Answer: 75000/1.25=60000.
Extended Worked Practice
Markup Followed By Discount

Question: A shop buys an item for $480, marks it up by 35%, then gives a 12% discount. Find the selling price and profit.

  1. Marked price =480(1.35)=648.
  2. Selling price =648(0.88)=570.24.
  3. Profit =570.24-480=90.24.

Answer: Selling price $570.24; profit $90.24.

Finding A Compound Interest Rate

Question: $5000 grows to $6050 in two years at a fixed annual compound rate. Find the rate.

  1. 6050=5000(1+r)^2.
  2. (1+r)^2=1.21.
  3. 1+r=1.1, so r=0.1.

Answer: 10% per year.

Tiered Utility Charge

Question: Electricity costs $0.18 per unit for the first 200 units and $0.25 per unit thereafter, plus a fixed charge of $12. Find the bill for 340 units.

  1. First 200 units: 200(0.18)=36.
  2. Remaining 140 units: 140(0.25)=35.
  3. Add fixed charge: 36+35+12=83.

Answer: $83.

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