If prices increase at a monthly rate of 0.8%, by what percentage do they increase in a year?

9.6% because 12 months in a year so 0.8 x 12 = 9.6

If the price at the end of each month is 0.8% greater than it was at the end of

the previous month, that means it's (1.008 times last month's price).

At the end of the second month, the price is

(1.008) times (the price at the end of the first month).

That's (1.008) ² times (the price at the beginning of the year).

At the end of 6 months, it's (1.008) ⁶ times (the price at the beginning of the year).

And at the end of 12 months, it's (1.008) ¹² times (the price at the beginning of the year).

(1.008) ¹² = 1.10 That's 10%greater than at the beginning of the year.

This is called 'compounding'. It grows faster than you might expect, because

each increase is a percentage of an amount that was already more than it was

when the year began.

The amount that prices rise is called "inflation". 0.8% in a month

sounds like a tiny, trivial, negligible amount that you don't even need

to think about. But if it keeps going for, say, 5 years, then prices have

increased by 61%! Any family whose income has not increased by that

amount is in big trouble. They are behind the 12.9-ball!