Ted intends to retire in 20 years. He expects that he will need to draw $30,000.00 a year from his savings account when he retires. He is about to set up a new retirement savings account that earns interest at a 3% annual interest rate (APR). He wants to make monthly contributions to the account from now until he retires.
1. How much money does Ted need to contribute to the account each month?
2. If Ted waits 5 more years to retire, what would his monthly payments be with under this same plan?
3. If Ted finds a plan that earns interest at 4% instead of 3%, how much will he have to contribute monthly if he plans to retire in 20 years?
Show your justification for every step in your solution.