You just won the lottery,and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?
A)6.72%
B)7.07%
C)7.43%
D)7.80%

Question

Quizplus · Accepted Answer

To calculate the rate of return built into the annuity, we can use the present value formula for an annuity:

PV = PMT * (1 - 1/(1+r)^n) / r

where PV is the present value of the annuity ($3,500,000 in this case), PMT is the payment per period ($500,000), r is the rate of return per period, and n is the number of periods (10 years).

Plugging in the numbers and solving for r gives:

$3,500,000 = $500,000 * (1 - 1/(1+r)^10) / r

r = 7.07%

Therefore, the best choice is to take the annuity, as the rate of return (7.07%) is higher than what could be earned through a low-risk investment like a savings account.

You Just Won the Lottery,and You Have a Choice Between