At the end of each month, interest of 1.3% of the amount in an account at that time is added to the account.
(a) Write down the difference equation satisfied by the amount An in the account at the end of the month n.
Hint: An will be equal to a multiple of An-1.
(b) Find the general solution to this difference equation.
(c) If the initial deposit is $1,219, determine how much is in the account after 4 years.
(d) Tom wants to save $23,000 to buy a new car. How many months will it take for Tom to achieve his goal? (Round your answer to the nearest month.)