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 | ||||

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