Bill deposits 10; 000 dollars every year in a savings account earning 3% a year com-
pounded annually. He makes the rst 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.

Question

Bill deposits 10; 000 dollars every year in a savings account earning 3% a year com-
pounded annually. He makes the rst 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.