Sumeet has a 16 year annuity that pays at the end of each year. The first payment is $2000 and the payments grow by R = 4% per year. Interest rates are r = 2% annually.

a) How much is Sumeet's annuity worth?

Consider the following two options:

Option A: An annuity with the same number of payments, only each payment is twice the payment of his current annuity.

Option B: An annuity where the initial payment is the same as his current annuity, the growth rate of the payments is the same, but he gets twice as many payments.

b) Without doing the computation, which do you think he would prefer? (No marks for this question, so feel free to take your best guess.)

c) Calculate the value of option A.

d) Calculate the value of option B.

e) What would your answer be if r = R?