Eric proposes a business transaction to his partners: they will give him $1000 now, and he will pay them back $2300 in one year, and finally they will pay him another $1400 in two years. He says because of compound interest it only looks like they're giving him more, but it's actually a fair deal. Show that there is no solution for the effective yield, and interpret what this means.

Some financial advisers view the golden ratio = 1+ 5 2 1.618 as an important number when determining how long to hold onto an investment. I swear I am not kidding, for example: Investopedia. Suppose you want to derive something like the "Rule of 70" but not for doubling time, but rather for the amount of time it takes until your initial investment C in a stock reaches the amount C, at which point you should sell. I reiterate that this is absolutely a real thing: Smithsonian Magazine. Compare the "Rule of 48" and the "Rule of 50" as an approximation for this time; when would one be better than the other?