Question

(4pts) 1. You just inherited some money, and a broker offers to sell you an annuity that pays $32,200 at the end of each year for 50 years. You could earn 8% on your money in other investments with equal risk. What is the most you should pay today for the annuity?

Answer 1

Present value of an ordinary annuity

Here, we’ve Annual Payment (P) = $32,200 per year

Annual interest rate (r) = 8.00% per year

Number of years (n) = 50 Years

Therefore, the Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

= $32,200 x [{1 - (1 / (1 + 0.08)⁵⁰} / 0.08]

= $32,200 x [{1 - (1 / 46.9016125)} / 0.08]

= $32,200 x [{1 - 0.0213212} / 0.08]

= $32,200 x [0.9786788 / 0.08]

= $32,200 x 12.2334846

= $393,918.21

“Hence, the amount that we should pay for this annuity will be $393,918.21”

Answer 2

SOLUTION :

Amount that can be paid should be at most equal to the PV of the annuity.

Annuity details :

Annuity amount, A = $32200 at the end of each year.

Period of annuity, n = 50 years

Return rate , r = 8% = 0.08

=> (1+r) = 1.08 

PV of annuity 

= A ((1 +r)^n - 1) / (r(1+r)^n)

= 32200(1.08^50 - 1) / (0.08*1.08^50)

= 393918.21 ($) 

So, amount that can be paid for the proposed annuity 

= at most $393,918.21   (ANSWER).