this is a tricky one indeed! At least to my knowledge, there is no simple way to calculate this with precision, unless the applied root happens to yield an integer (here not the case). But it also doesn't matter.
While I'm of course not aware of the exact context, I can share what typically works in such situation.
Firstly, (any reasonable) MBB interviewer would not expect you to calculate an exact CAGR over 5 years manually in a live interview scenario, given the complexity of the computation without access to a calculator.
That said, you can always give an rough approximate. Management consulting is not an exact science, which is why an 80/20 type of approach is typically enough (esp. in a back-of-the-envelope), as long as the answer / recommendation does not change. The steps to do this can be as follows:
- Check with the interviewer if he/she needs exact solution and propose a quick & dirty approximation instead (you'll actually score plus points for practicality + problem-solving right there!)
- Calculate the approximation:
- Get overall percentage growth 232/171 = 35%
- Divide by no. of years (5) to get linear growth = ~7%
- Apply a discount of 0.5-1% to account for the compounding effect
- Give range as answer to appreciate the inaccuracy of the heuristic (~6-7%) and qualify again (say you ofc could verify exact # with a calculator for exact result, but it won't change the overall answer)
In 99% of the cases, an interviewer will be more than happy with this approach and answer and appreciate the practicality of the approach. I certainly would have been.
Hope this helps. Do feel free to send me a PM, if you have further questions.