Is there a difference in DDR3 1600 Mhz and 2133 Mhz memory in a PC for work?

Question

AMD

Hello!
BACKGROUND:
I am a web developer.
I built a PC more than 4 years ago, I still work on it.
PC specifications:

• cpu: AMD Phenom ii x4 b60 (3.4 GHz)
  
• ram: 8GB DDR3 (1333MHz) Team Elite
  
• GPU: Nvidia GTX 650 Ti (Palit)
  
• mb: ASUS M5A78L-M Plus/USB3
  
• ssd: 250 GB (Samsung)
  
• dp: 22'' 1920x1080
  
• OS: Ubuntu 16.04.5
  

A PC is more than suitable for work.
They are pleased.
ESSENCE:
Now you need to assemble a similar PC for an employee.
I also decided to build on the AMD platform.
Already ordered:

• CPU: AMD Athlon X4 870K (3.9GHz)
  
• mb: Asus A68HM-K
  
• ssd: 250 GB (Samsung)
  

The selected processor and motherboard support memory up to 2133 MHz.
I think what memory to buy.
I will definitely take 1 bar for 8 GB (in order to buy another 8 GB later).
I doubt only the memory frequency, because 1333 Mhz and 2133 Mhz are quite different in cost. I think it would be optimal to take 1600 Mhz.
QUESTION:
Do you think it makes sense to overpay for memory with a higher frequency (for example, 2133 MHz) or is it better to take 1600 MHz? After all, a budget PC, purely for work. And it is not clear whether the difference in memory frequency will be noticeable in the work under Ubuntu (as opposed to its price, which is noticeably different).
PS. Those wishing to write comments like: "it was better to assemble on Intel, please refrain." The question is only about memory, the processor has already been ordered. Anyone with knowledge of the subject would appreciate your advice.

Answer 1

The difference will not be noticeable.

Answer 2

The frequency of the RAM affects its maximum possible speed (At the same time, the CPU and the mother must support this frequency)
But do not forget about the timings, the lower the timing , the faster the memory
Growth calculator: https://notkyon.moe/ram-latency.htm ( I'm not sure if he thinks correctly)
Wiki recommends this(CL/(частота-MHZ) * 1000) = тайминг в нс