Could you please clarify why we divide 1.04 instead of multiplying it when calculating the number of first-grade students in the US? I would assume that with a positive growth rate, we should multiply to obtain the number of students who will buy the new textbook in the next year.
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Hi there,
Thank you very much for this question. I would be happy to share the solution to it:
- Since we want to calculate the number of children born 7 years ago, a number in the past, we need to divide by this positive growth rate instead of multiplying by it.
If you would like a more detailed discussion on how to best prepare for your upcoming interviews, please don't hesitate to contact me directly.
Best,
Hagen
Hi there,
Hagen is exactly right here.
This is a super rare situation and I personally have not seen this in a case. That said, it's good to know, and, most importantly, it's always good to practice how to react to a new thing mid-case…using logic and math fundamentals you could have tried to figure it out. Practice these scenarios as you are likely to get something you havenm't seen before, and therefor cannot solely rely on memorization!
Great to see that you already received a clarification for the question.
Sharing here a guide that you might find useful with the most common formulas and terms that show up in interviews:
Best,
Cristian
Because you are trying to take out the growth (to estimate a number in the past) istead of projecting growth to estimate a number in the future.
1. The assumption is that the population of 350 million is uniformly distributed across all age groups, with a life expectancy of 75 years. Under this simplification, each age cohort contains approximately 350 million/75 age groups.
2. For the sake of the exercise, factors such as migration, changing birth rates, and demographic aging are explicitly ignored.
3. At the same time, it is given that the total population grows by 4% per year. Under the same simplification, this growth must be assumed to be distributed proportionally across all age groups.
As a result, our starting point is a population snapshot of 350 million people today, of which roughly 1/75 are seventh graders. We are evaluating an investment opportunity for next year, when the population is expected to be 4% larger. Consequently, the expected number of seventh graders should also increase by approximately 4%.
The key mistake is that different time horizons are being mixed together inconsistently. If we accept the assumptions of a growing population and a uniform age distribution, then a smaller seventh-grade cohort in the following year would be logically inconsistent with those assumptions. By simple causality, population growth implies that the size of each age cohort grows proportionally when all other demographic effects are intentionally abstracted away.
Of course, this would not necessarily hold in the real world, where birth rates, migration flows, mortality patterns, and changes in life expectancy can significantly affect the size of individual age groups. However, those complexities were explicitly excluded from the problem, so the simplified model should be applied consistently throughout the analysis.