Bill deposits 10,000 dollars every year in a savings account earning 3% a year compounded annually. He makes the first deposit at his 25th birthday. He makes deposits until his 45th birthday. After this point, he does not deposit or withdraw money from the account until he is 65 years old.
1. Let Mn be the amount of money in thousands of dollars in Bill's savings account after n years. Find an expression for M0, M2 and M3.
2. Find a closed form expression for how much money Bill has in his savings account at his 45th birthday.
3. Find a closed form expression for how much money Bill has in his savings account at is 65th birthday.
I'm having a TON of help with this, I just can't figure it out. I can figure out a recursive formula for it (Mn = 10 + .03(M(n-1)) or Mn = (1.03)(10+M(n-1)) ), but I just don't know what to do. What's the difference between an "expression" and a "closed form expression"? Is the recursive formula I figured out good enough for part 1 (if I fill it in with the appropriate years, of course)? But then what do I do for the last two parts? What's the difference there? I can't seem to figure out how to make this a geometric series, or fit any type of series formula or anything that we've been learning about.
Please help me!
Also, by the way, I'm new here. I'm a college freshman in calc 2, which is where this question is coming from! Thanks for any help.