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I'm considering 2 general scenarios of both having an average salary increase of 6% over 5 years. But in the first scenario, the person ends up with a lower total salary compared to the second scenario. Why? I can't seem to wrap my head around it...

Please check out the image, I have both scenarios in an Excel doc. enter image description here

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3 Answers 3

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When you get bigger increase sooner, you have it for more time, and so end up with more total money.

I think it's simpler to consider shorter case. If you work for 2 years, initially for 1 dollar / year, and you get one increase of 100% - then if you get the increase immediately, you get 2 dollars twice, for a total of 4 dollars. If you get your increase after the first year, you get just 3 dolllars. And if you get increase after the second year, you got 2 dollars in total, as your new salary didn't have any effect yet.

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  • $\begingroup$ That's a great explanation, I really appreciate it! $\endgroup$
    – sheavictoria
    Commented May 10 at 17:48
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It becomes apparent when you take this scheme to the extreme:

  1. given them 4 years no increase, then 30% for the last year.

vs.

  1. Give them a 30% increase for year 1, then no increase the remaining 4 years,

Both scenarios lead to the same end salary, but in scenario 2) they got this high salary for 5 years, while in scenario 1) only for 1 year. So scenario 2 is much better for the employee then scenario 1.

Your example is similar, just not as extreme because your split of the 30% increase over time is more gradual. But like in my scenarios, the one having the higher initial increase has the better final result.

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  • $\begingroup$ Great example, thank you! $\endgroup$
    – sheavictoria
    Commented May 10 at 17:55
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Note that the final salary is the same. This is because multiplication is associative and commutative. An increase of $n \%$ is actually multiplication by $1 + n/100$ so the order of the increases has no effect on the final value. However, you cannot deduce from this that the total earned over the period will not be affected.

As mihaild says, the sooner you get the bigger increases the better. Here are two simple examples which might make this clear.

  1. Your boss says: you are going to get a $10 \%$ increase, do you want it this year or next?

  2. Your boss says: you can have a $10 \%$ increase this year and $20 \%$ next year or $20 \%$ this year and $10 \%$ next year, which do you want?

In both scenarios, your final salary will be the same but what would be your choices and why?

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    $\begingroup$ I like the 2 examples you give, super helpful! $\endgroup$
    – sheavictoria
    Commented May 10 at 17:54

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