Question: This question consists of the following three independent parts.
(1) John plans to retire in 15 years, and he wants to have an annuity of $50,000 a year for 20 years after retirement. John wants to receive the first annuity payment at the end of the 15th year from today (the same day as his retirement date). How much must John invest today in order to have his retirement annuity if the annual interest rate is 6%?
(2) How long would it take to accumulate $1 million if you begin putting $100 in the bank every week starting one week from now at an EAR of 8% with weekly compounding? There are 52 weeks in a year.
(3) Jen is going to deposit $250 into an account at the beginning of each of the next 5 years starting today. The account will then be left to compound for another 10 years (between the end of year 5 and the end of year 15). At the end of year 16, Jen will start receiving perpetuity from the account. If the account pays 7% annually, how much each year will she receive from the perpetuity?