What on earth ... where are you getting these percentages? I'm by far the greatest at math (3 x 6 = blue) but I read your mathplay link and I see it differently - as in exactly what the link says... a 1.25% raise at year one is still a 1.25% raise at year 4... you just add the 1.25 from year 1 to the base of year 2, and then again for year 3 and so on...

Not really, they compound each year. It's not very dramatic because the rate is pretty low. But it will result in a noticeable difference against your monthly rates if you don't compound the raise each year, and why the total raise is slightly higher than just straight adding 1.25 each year.

So initially, you are at your standard rate of 1

each year you multiple by 1.0125 to give you your raise (1+ 1.25%= 1+0.0125). This gives you your overall new pay rate. (if you just want to see how much your new pay rate increase is going to be, you can just multiply by 0.0125 a year, which is 1.25% as a whole number)

so your first raise is

1.00 * 1.0125 = 1.0125 (*base pay)

second year you multiply the raise (1.0125) times the

rate from the previous year, not the original1.0125 * 1.0125= 1.0252

1.0252 * 1.0125 =1.038

...

etc

you do the same each year, and after 4 annual 1.25% increases, are at a 6.41% raise instead of 6%.

If you go to the link, they explain the compound interest formula. Basically every time it compounds, you are starting with a slightly larger bit than you had last time.

future value = present value x (1+interest rate) ^ number of periods

you can plug in the numbers, but the interest rate is 1.25% = 0.0125, and there are 5 periods (counting from 2013 to 2017).

It's only a small difference, but only because of how small the annual increase is. If you have larger increases, or more regular increases, that's how you get into trouble with compound interest rates, and why your balance will quickly build up on a credit card if you don't at least pay the minimum each month.

A more extreme case is when something doubles each time (for example cells that split). You start with 1, then 2, then 4, 8, 16, 32, etc.

That's the same as a 100% compounding interest rate (ie 1), or working it into the formula;

fv = present value x (1 + 1)^number of periods

So if you start with 1, and go through 4 cell divisions (ie 4 periods) the math is

FV= 1 x 2^4 = 16

It's nice to have compounding interest work for us for a change with a raise, instead of against debt.