only need Q9

Everything is the same as Question 4. However, you now deposit $10,000 into the account in the first year, and your deposit increase at 1% every year (so the second deposit is $10,100, the third is $10,201 etc). What rate of return do you need to earn on the account so that your constant annual annuity income is $100,000? Starting on 1st January 2020 , you deposit $10,000 into a bank account for 35 years (so until 1st January 2054). The bank account earns 7% interest. On 1st January 2055 , you use all the money in the account to purchase a life annuity. The life annuity is priced assuming that (1) your mortality is that of a male in 2017 according to the SS mortality table I have given you in class (2) that you are 65 years old on 1st January 2055 (3) you receive one constant, non-increasing payment on 1st January every year until you die, starting on 1st January 2055, and (4) interest rates after 2055 are 4% p.a.. What constant annual income will you get from the life annuity