Answer:
no, you shouldn't take the offer because the present value of your prize is higher than $35 million.
Explanation:
we must first calculate the present value of the annuity in 6 months. The effective interest rate per year = (1 + 9%/365)³⁶⁵ - 1 = 1.094162145 - 1 = 0.094162145 = 9.4162145
the discount rate for every 6 months:
0.094162145 = (1 + r)² - 1
1.094162145 = (1 + r)²
√1.094162145 = √(1 + r)²
1.046022058 = 1 + r
r = 0.046022058 = 4.6%
now the present value of the annuity in 6 years = $1,900,000 x (annuity factor, 4.6%, 40 periods) = $1,900,000 x 18.14185 = $34,469,515
then we must find the present value = $34,469,515 / 1.046 = $32,953,647.23
the total value of your prize = $32,953,647.23 + $5,500,000 = $38,453,647.23
