"Suppose your great$-$grandfather had purchased a violin in $1889$ for $$125$ as an investment. The family held on the violin for $134$ years, and it was recently sold for $$100,000.$

What was the average annual compounded rate of return on the $$125$ investment? Calculate the annual rate of return.

Was the violin purchase a good investment? Why?

Would your answer change if the average stock market return $($Dow Jones Industrial$)$ return was $10\%$ per year? Why?