samuel is $25$ years old and wants to retire at age $50$ and travel the jungles of the world l$.$ he believes he will contract some deadly tropical disease and die at the age of $70.$ samuel estimates that he will need $$8,000$ per month to live like he wants to in the jungle. assuming that samuel can earn $12\%$ during his working years and $8\%$ during his retirement years how much must he invest each month until he retired?