MHB Basic problem about investment (basic percentages, and econ/finance).

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Liam and Ben have differing inflation expectations, with Liam predicting 5% and Ben 4%. They are considering two investment options: Fund 1, which offers an 8.6% return, and Fund 2, which provides a return based on the CPI rate plus 3.75%. If inflation is 5%, Fund 2 yields 8.75%, making it a better choice for Liam, while at 4% inflation, Fund 2 yields 7.75%, which is less favorable for Ben compared to Fund 1. Therefore, Liam should invest in Fund 2 and Ben in Fund 1 for optimal returns based on their inflation forecasts.
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Liam and Ben are two friends who started studying the world of Finance and have different expectations for inflation in the coming years. Liam estimates inflation of 5% per year and Ben estimates inflation of 4% per year. Suppose they have the following options available for investment:
  1. Fund 1, which pays a rate of 8.6% per year;
  2. Fund 2, which pays a CPI rate (inflation rate) + 3.75% per year.
What should they do?

a) Liam should invest in fund 1 and Ben in fund 2

b) Liam should invest in fund 2 and Ben in fund 1

c) both must invest in fund 1

d) both must invest in fund 2
 
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Let the amount invested be A.
Investing in Fund 1 pays 0.086A.

If inflation is 5%, investing in Fund 2 will pay 0.0875A which is more than 0.086A.
If inflation is 4%, investing in Fund 2 will pay 0.0775A which is less than 0.86A.

Liam should in fund 2 and Ben should invest in fund 1.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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