The price of gold increased by 20%. Shortly afterward, the new price decreased 20%. Francesca says the price is "right back where it started." Is Francesca correct? Use an example to explain.

Question

The price of gold increased by 20%. Shortly afterward, the new price decreased by 20%. Francesca says the price is "right back where it started." Is Francesca correct? Use an example to explain.

Answer 1

Let's call the initial value of gold G. When the value increases by 20%, the new value is 1.2G. When we decrease this value by 20% the value changes to 80% of this new value=0.8*1.2G=0.96G. So it hasn't returned to its former value! You can see it all depends on what you base the percentage. Francesca was wrong. It's lower than where it started.