Your goal is to have an annuity that pays you $50,000 a year for 20 years with the first payment occurring 15 years from today (i.e. end of year 15). To achieve this goal, you plan to deposit each year into an account, for the next 14 years, a sum that will compound annually at 8%.
a. What is the dollar amount of the annual deposit that, at the end of year 14, achieves your goal (assume constant end of year deposits)?
b. Suppose now, that at the end of the fifth year (i.e. five years from today) you know you will be given a gift of $20,000 which you will deposit into your account at that point. In addition to this deposit, how much do you now need to deposit annually such that, at the end of year 14, you achieve your goal (assume constant end of year deposits)?