What is compound interest

Compound interest works like this:
If you put £100 in the bank at 5% per annum interest, it means you get 5% each year.
After 1 year you get £5 interest so now have £105.
In the second year you get 5% interest, but this is now 5% of £105 not of your original £100, so it is £5.25 and your total goes to £110.25 and so on.

Now for calculations: (I'll use the same numbers)
You have to remember / know that adding 5% is the same as multiplying by 1.05

So year 1: 100 * 1.05 = 105
year 2: 100 * 1.05 * 1.05 = 100 * 1.05^2 = 110.25
year 3: 100 * 1.05 * 1.05 * 1.05 = 100 * 1.05^3 = 115.76

You can see that for year x you have 100*1.05^x
For any starting amount A and interest r% you are getting after year x: A*(1+r)^x

If you have, say £147.75 in the bank then
147.75 = 100*1.05^x
1.05^x = 147.75/100 = 1.4775
x = log_(base1.05) 1.4775 which you can do on some calculator directly

If you can't on your calculator, then you can do
1.05^x = 1.4775
ln(1.05^x) = ln(1.4775)
x ln(1.05) = ln(1.4775)
x = ln(1.4775) / ln(1.05)
x = 8

Hope that helps

Attached is a link for various compound interest formulas...including ones which incorporate "powers"