Chapter 9.1, Problem 43ES

Each year on his birthday Tim’s grandmother deposits $\text{\$20}$ into a “birthday account� that earns an annual interest rate of 10%. The year’s interest is added to the account at the same time as that year’s deposit.

(a) Let $a_n$ denote the amount in the savings account after n years with $a_0=20$ (dollars) the very first deposit on the day of Tim’s birth. Find a recursion formula for $a_n{}_{+1}.$ (Assume that no money is ever withdrawn from the account.)

(b) Use the formula from part (a) to determine how much money will be in the account when Tim is 40 years old.