Question

If prices increase at a monthly rate of 3.9​%, by what percentage do they increase in a​ year?

Answer 1

The answer is: 0.468 as decimal or 46.8%

Explanation:

Since the prices increase at a monthly rate of 3.9% per month. To find the percentage do they increase a year, we need to convert 3.9% to a decimal.

So here how we do it. We put 3.9 percent on the numerator because it a small number which is what we want over 100 like this:

`3.9/100`

Now when plugging this into your calculator you get: `0.039`.

So what do we do with this number?

We now times it by 12 like this: `0.039*12` which gives us:

`0.468`

So we can convert this back to a percentage by moving the decimal by 2 places to the right which gives us 46.8%.

Another way we could of done this without doing the long way to figure it out is by multiplying 3.9 times 12 which still gives us 46.8%

Answer 2

`58.27%`

Explanation:

The easiest way to do this is:

If something is increasing at 3.9% per month, then after one month you have 103.9% of something. This includes the 100% you started with.

So after each month you have:

`(103.9/100) * (103.9/100) * (103.9/100)` etc. This will occur 12 times:

`:.`

`(103.9/100)^12=1.582656154`

This is in decimal form, so:

`1.582656154*100=158.2656154%`

Subtract the `100%` you started with:

`58.27%` 2 d.p.