An insurance agent is trying to sell you an immediateretirem

?An insurance agent is trying to sell you an? immediate-retirement annuity, which for a single amount paid today will provide you with 19,700 at the end of each year for the next 15 years. You currently earn 9?% on? low-risk investments comparable to the retirement annuity. Ignoring? taxes, what is the most you would pay for this? annuity?

Solution

the maximum amount payable for annuity will be the present value of annuity:

present value of annuity = P [ 1 -(1+r)^(-n)] / r.

here,

P=$19,700

r=9%

=>0.09.

n = 15 years.

=>$19,700[1-(1.09)^(-15)]/0.09.

=>$19,700 [0.725462/0.09]

=>$19700[8.0606889]

=>$158,795.57

the most that can be paid =$158,795.57.