Why is this way of calculating the same percentage giving different results?

Question

Where I come from the employer must deduct 9.5% of your gross wage pre tax, to pay into a fund we call superannuation.

My daily gross rate is 450 before tax. 9.5% of 450 is 42.75. I get paid fortnightly so 42.75 * 10 working days = 427.50 paid into my super account per fortnight.

I contacted my employer about this and he said that I am calculating superannuation wrong. In his own words:

450 / 1.095 = 410.96
450 - 410.96 = 39.04
39.04 * 10 working days = 390.40

The 390.40 is what is on my payslip each fortnight. I don't understand how 9.5 percent of 450 can be 42.75 but 450 - (450 / 1.095) = 39.04.

Is 450 / 1.095 the correct way to calculate 9.5 percent of 450?

Interestingly, the government tool I am using to check this: https://www.moneysmart.gov.au/tools-and-resources/calculators-and-apps/employer-contributions-calculator comes up with the same answer as me.

Help please :S

Answer 1

I'm referring to the following written by chap in a comment above:

The contract states "450 per day inclusive of super."

In that case, your employer seems to be right. You get compensation in 2 forms: The daily gross rate ($g$) and the payment to the superannuation fund ($f$). What you and your employer agree on is that:

$$ f=0.095g$$

What you disagree on is what value correspondes to the 450$/d (I assume that currency just to have a meaningful unit).

You think $g = 450\$/d$ (450 Dollar per day). They think (and calculate) $g+f = 450\$/d$. Because the contract says "inclusive of super(annuation)", I'd say they are right.

Answer 2

Imagine it were $£100$. $9.5$% of this is clearly $£9.50$. Yet via the employer's method, $$\frac{100}{1.095}=£91.3242...\to £91.34$$ Considering that this value is being subtracted, you're losing rather a lot.