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?

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a

$117,225.73 every year

b

$117,225.74 every year

c

$117,225.75 every year

d

$117,225.76 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?

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a

$97,929.30

b

$97,929.31

c

$97,929.32

d

$97,929.33

Question 6

Everything is the same as in Question 4 but your mortality rates are now 20% higher than a male of your age in 2017. The income you will get from the annuity is now:

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a

$123,976.22

b

$123,976.23

c

$123,976.24

d

$123,976.25