(Use the information from question 4 to answer question 9)

Question 4

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?

Answer: $117,225.75 every year

Question 9

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?

a. 5.76%

b. 5.77%

c. 5.78%

d. 5.79%