Discount, tax and simple interest

A discount is subtracted

A bag marked at $80 has a 15% discount. The discount is 15/100 × 80 = 12 dollars. The sale price is 80-12 = 68 dollars. Giving 12 as the price confuses the saving with the amount to pay.

You can find the remaining 85% directly: 0.85 × 80 = 68.

Tax is added to the stated base

In this example, a shop states that 8% GST is added to a pre-tax price of $50. This is a rate supplied for the exercise. GST is the percentage tax stated in this problem. The tax is 0.08 × 50 = 4 dollars and the total is $54. Use the rate and charging order in the problem rather than assuming a current tax rule.

If a $100 item is discounted by 10% and then 8% tax is charged on its discounted price, the discounted price is $90. Tax is 0.08 × 90 = 7.20 dollars, so the total is $97.20. The second percentage uses a different base from the discount.

Before calculating, write a short chain of bases: marked price → sale price → price with tax. A discount removes a percentage of the marked price; tax is added to the base the question states. Do not combine the rates before identifying those bases.

Check your understanding 1 Separate the tax from the bill

A service costs $75 before GST. The problem states a GST rate of 6%, charged on that price. Find the GST amount and the final bill. Use this supplied rate.

Your GST amount and final bill in dollars

Show answer

GST is 6/100 × 75 = 4.50 dollars. The bill is 75 + 4.50 = 79.50 dollars. The bill represents 106% of the pre-tax price. Giving $4.50 as the bill would leave out the original cost; multiplying 75 by 6 would leave out “per hundred”.

One year’s simple interest

A stated annual simple-interest rate of 3% on $400 gives 0.03 × 400 = 12 dollars of interest for one year. The balance becomes $412. Interest and final balance are different quantities. For simple interest over two years with the original principal unchanged, each year earns $12: $24 altogether.

Check your understanding 2 What amount is the percentage of?

A $60 item has a 25% discount. A stated 10% service charge is then calculated on the sale price. Find the final bill.

Your answer or drawing on paper

Show answer

The discount is $15, leaving $45. The service charge is 10% of $45, or $4.50. The final bill is $49.50. Calculating both percentages on $60 would use the wrong base for the charge.

Check your understanding 3 Interest or balance?

A deposit of $650 earns simple interest at a stated annual rate of 2%. It stays unchanged for one year. Find the interest and the balance after that year.

Your interest and balance in dollars

Show answer

One percent of $650 is $6.50, so 2% is $13. The balance is 650 + 13 = 663 dollars. Equivalently, 0.02 × 650 = 13. The principal is the whole used for this year’s interest, and the balance includes that principal. The rate does not mean $2 of interest.

Check a suggested principal

An account earns $18 interest in one year at a stated 2% simple-interest rate. Check whether an original deposit of $900 fits this information.

Your calculation and conclusion