Question

Your uncle named you beneficiary of his life insurance policy. The insurance company gives you a choice of $100,000 today or a 12-year annuity of $12,000 at the end of each year. What rate of return is the insurance company offering?

Answer 1

Answer: 3.085% per year

Step-by-step explanation:

P = 100000

F = 12*12000 = 144000

t = 12

144000 = 100000(1 - r)¹²

144000/100000 = (1 - r)¹²

1.44 =  (1 - r)¹²

log 1.44 =  log (1 - r)¹²

log 1.44 =  12 log (1 - r)

0.158362 = 12 log (1 - r)

0.158362/12 = log (1 - r)

0.013197 = log (1 - r)

10⁰.⁰¹³¹⁹⁷ = 1 - r

1.03085 = 1 - r

r = 1.03085 - 1

r = 0.03085

r = 3.085 %