(Use information in questions 4 & 5 to answer question 8)

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 5

Everything is the same as in Question 4, but the annuity you buy has COLA's of 2% per annum. (That is, the payments increase every year by 2%). What is the initial value of the income you receive from the annuity on 1st January 2050?

Answer: $97,929.32

Question 8

Everything is the same as Question 5. What interest rate do you need to earn on the bank account so that your first annuity payment (received on 1st January 2055) is $100,000, increasing at 2% p.a. thereafter?

a. 7.07%

b. 7.08%

c. 7.09%

d. 7.10%