I'm more sophisticated than my little sister. I save my money in a bank account that pays me 3% interest on the money in the account at the end of each month. (If I take my money out before the end of the month, I don't earn any interest for the month.) I started the account with $50 that I got for my birthday. How much money will I have in the account at the end of 10 months? How many months will it take to have at least $100? Justify your answer with a mathematical model of the problem situation.