Suppose you just won the state lottery,and you have a choice between receiving $3,025,000 today or a 20-year annuity of $250,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.
A) 5.62%
B) 5.35%
C) 3.95%
D) 6.65%
E) 6.34%

Question

​Suppose you just won the state lottery,and you have a choice between receiving $3,025,000 today or a 20-year annuity of $250,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.
A) ​5.62%
B) 5.35%
C) 3.95%
D) ​6.65%
E) ​6.34%

Quizplus · Accepted Answer

We can use the present value formula to determine the rate of return built into the annuity:

PV = [PMT x (1 - (1 + r)^-n)] / r

Where:
PV = present value ($3,025,000)
PMT = payment per period ($250,000)
r = interest rate per period (unknown)
n = number of periods (20)

Plugging in the values, we get:

3,025,000 = [250,000 x (1 - (1 + r)^-20)] / r

Solving for r using a financial calculator or Excel, we get:

r = 5.35%

Therefore, choosing the annuity with a 5.35% rate of return would be the best choice since it has a higher present value than the lump sum of $3,025,000. However, other factors such as personal financial goals and tax implications should also be considered.

​Suppose You Just Won the State Lottery,and You Have a Choice

Suppose You Just Won the State Lottery,and You Have a Choice