Mathematics
Interest & discounts
What does the jacket really cost with 30% off? And what does the bank do with your money? Percentages in everyday life.
What you need first
Sale signs in shop windows, interest on your savings account, VAT on the receipt: wherever money is involved, percentages show up. If you can calculate them confidently, you spot real bargains, see through marketing tricks, and know what you'll actually pay in the end.
Discount: subtract the percentage amount
A 20% discount on 50 euros means: first work out the percentage amount, that is 20% of 50 euros = 10 euros. Then subtract this amount from the original price: 50 − 10 = 40 euros. The original price is called the , and it's always what the percentage refers to. In word problems, look carefully at what the percentage refers to: that's the base value, and it always corresponds to 100%.
Interest and VAT: add the percentage amount
Interest works like a discount in reverse: the bank calculates a percentage of your balance and adds it on top. Interest rates are almost always given per year. With 500 euros and 2% interest per year you get 10 euros extra after one year, leaving you with 510 euros. VAT works the same way: in Germany, usually 19% is added to the net price. A net price of 100 euros becomes 119 euros. Whether you subtract or add: the first step is always the same, working out the percentage amount from the base value.
Careful with stacked discounts
First 20% off, then another 10%: that is NOT 30%. The second discount applies to the already reduced price, so to a smaller base value. 100 euros first becomes 80 euros, and 10% of that is only 8 euros. In the end you pay 72 euros, so the total discount is 28%. Remember: after every step there is a new base value.
Backwards: from the final price to the base value
Sometimes only the reduced price is on the tag and you want to know what the item cost before. After a 20% discount, a backpack still costs 60 euros. After the discount, 80% of the base value is left, so those 80% are the 60 euros. Divide by 80 and you know 1%: 0.75 euros. Times 100 gives the base value, namely 75 euros. Going through 1% as a stepping stone takes you from any percentage to any other.
Exercises
0 of 6 solvedTime to try it yourself. You can't break anything, every attempt counts.
A t-shirt costs 50 euros and there is a 10% discount. How many euros do you save?
A game costs 80 euros. There is a 25% discount. What do you pay (in euros)?
You deposit 200 euros at 5% interest per year. How many euros of interest do you get after one year?
Match each term with the right description.
A savings account holds 500 euros at 2% interest per year. How many euros are in the account after one year?
With two discounts in a row, the second discount refers to the … price.
Where this leads