Question

You have won the lottery. You will receive $5,500,000 today, and then receive 40 payments of $1,900,000. These payments will start one year from now and will be paid every six months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $35 million. If the appropriate discount rate is an APR of 9 percent compounded daily, should you take the offer

Answer 1

no, you shouldn't take the offer because the present value of your prize is higher than $35 million.

Step-by-step 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