# Inflation

*Keywords:*

AO elaboration and other teaching resources

Estimate and find percentages of whole number and decimal amounts.

Number Framework Stage 8

#### Using Number Properties

Problem: “Today the price of an ice cream in the country of Nuldova is $1.50. Prices are rising at a rate of a 100% per year. What will be the price of the same kind of ice cream in 20 years time?”

Discuss why 100% increase means doubling the price each year.

*(Answer: 100% increase means the price is 200% of the original, that is, double.)*

Discuss why prices are $1.50, $3, $6, $12 ... and how to enter this on a calculator.

*(Answer: Enter 1.50 *x *2 = = = = counting 20 equal signs, which gives $1,572,864.) **Note: Some calculators require the user to go: 2 *x *1.5 = = = = .... Carefully check **which system your calculators use before attempting this problem.)*

On some calculators, you can also use the y^{x} button to get the answer.

*(Answer: Enter 1.50 *x *2 y*^{x} *20 = into the calculator.)*

Example: In a country with inflation of 10% per year what will be the price of a $20,000 new car in 40 years time?

*(Answer: 20 000 *x *(1.1)** ^{40} *≈

*$905,185.)*

Problem: “In a country where inflation is running wild at 56% per year, how long will it take for a $1 ice cream to cost $1,000,000?”

Discuss why entering 1.56 as a constant multiplier in a calculator is sensible. Get students to enter 1.56 x = = = = and count carefully.

*(Answer: If, for example, the equals button has been pressed 4 times, the answer to **1.56 ^{5} is in the display not 1.56^{4}. When 1.56^{31} has been entered, the display shows *

*970202.8566, and when 1.56*

^{32}has been entered,*the display shows 1513516.456. So the cost reaches $1,000,000 in just over 30 years.)*

Examples: For these rates of inflation, find out how long it will take a $1 ice cream to

cost $100,000,000: 99%, 87%, 300% , 50% , 1 000%

#### Understanding Number Properties:

If inflation is running at 10%, Gerry argues prices will double in 10 years. Explain why Gerry thinks this. Explain why Gerry is wrong. *(Answer: Gerry says 10 *x *10% = 100%, so the price increase by itself, that is **to say doubles, in 10 years. But he is wrong. Adding 10% to, say, $1 gives a price of **$1.10. For the next year, 10% is added to $1.10 not $1 to give $1.21. So the 10% **added each year is being added t o an increasing amount every year, so prices will **double in less than 10 years.)*