Given that average inflation from 2014 until 2024 is 4%, how big increase in nominal salary you would need in order for your real salary to increase 30% from 2014 until 2024?


Assume that your salary is $x$ dollars per year in 2014 (that's both nominal and real). Now, let's suppose that in 2015, all prices inflate by a factor of $r$. That means that the buying power of your salary declines by a factor of $r$ from 2014 to 2015 - you're still earning $x$ nominal dollars, but only $x/r$ real dollars. At this rate, you'll find you're only earning $x/r^{10}$ real dollars in 2024.

You want to be earning $1.3x$ real dollars in 2024. Hence, we need to figure out how large a nominal raise $\delta$ you need to get in order to achieve your desired salary. In other words, we must solve:

$$1.3x = \frac{x}{r^{10}} + \delta$$

for $\delta$. This is straightforward:

$$\delta = \left(1.3 + \frac{1}{r^{10}}\right)x$$

Hence, you need a nominal raise in the amount of $1.3 + \frac{1}{r^{10}}$ times your 2014 salary ($x$) in order to get a $30\%$ increase in your real salary by 2014. Plugging in $r = 1.04$, we find that your nominal salary must increase by a factor of $\boxed{1.98}$ over 10 years.

If, instead of having the raise as a one-time bulk increase, you want to have a percentage raise each year, we can compute the needed yearly raise $d$ as follows:

$$d = 1.98^{1/10} = 1.07$$

Hence, you must have a nominal yearly raise of $\boxed{7\%}$ in each of 2015, 2016, ..., 2024 in order to achieve a $30\%$ increase in real wages by 2024.

  • $\begingroup$ Don't you make a sudden jump from 2014 to 2024 ? What happens between these two years ? $\endgroup$ – Claude Leibovici May 4 '14 at 6:32
  • $\begingroup$ @ClaudeLeibovici Sorry, are you saying that my explanation is inadequate or that my solution is incorrect? $\endgroup$ – senshin May 4 '14 at 6:33
  • $\begingroup$ I don't say that but the way I understood the question is : what are the raises in 2014, 2015, 2016, ..., 2024 in order to earn 30% more. I honestly don't know and I shall wait for your analysis. $\endgroup$ – Claude Leibovici May 4 '14 at 6:49
  • $\begingroup$ @ClaudeLeibovici Oh, I see what you're saying. I'll update the answer in case OP wanted a year-over-year raise rather than a single lump-sum. $\endgroup$ – senshin May 4 '14 at 6:50
  • $\begingroup$ This is what I meant and how I understood the post. Cheers. $\endgroup$ – Claude Leibovici May 4 '14 at 6:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.