Question

Atlas Insurance wants to sell you an annuity which will pay you $550 per quarter for 30 years. You want to earn a minimum rate of return of 5.0 percent compounded quarterly. What is the most you are willing to pay as a lump sum today to buy this annuity?

a.$31,207.66

b. $32,868.16

c. $32,411.57

d. $33,819.39

e. $34,090.57

Answer 1

The maximum payment which can be paid is PV of annuity stream.
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	550 per quarter
r = the effective interest rate (also known as the discount rate)	5% per annum or 1.25% per quarter
i=nominal Interest rate
n = the number of periods in which payments will be made	30 years or 120 quarters
PV=	PMT x (((1-(1 + r) ^- n)) / i)
PV=	550* (((1-(1 + 1.25%) ^- 120)) / 1.25%)
PV=	34,090.57
So option E is correct