You are opening a savings account that earns compound interest. which compounding frequency will earn you the most money?

In general, it is true that if the frequency is higher, then you make more money. For example, suppose you have a capital 1$ and the interest rate can be either 50% compunded annually or 25% compounded semiannually (same total interest in a year, different compounding rate). In the first case you get 1.5$ back at the end of the year, while in the second case after 1 semester you have 1.25$. After 2 semesters, you have 1.56$. You cannot make infinite money this way though; you can at most gain a factor of 2.7 by reducing the intervals of compounding.
The correct answer is the highest frequency, namely when the interest is compounded as frequently as possible (as long as the total interest rate is the same).

Renting provides greater flexibility but can lead to higher costs in the long-term.

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