Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or $250,000 a year for 20 years, with the first payment starting one year from today. What annual interest rate does the second choice provide?
A) 7.12%
B) 7.49%
C) 7.87%
D) 8.26%

Question

Quizplus · Accepted Answer

The second choice is essentially an annuity, where you receive $250,000 annually for 20 years. To find the interest rate, we can use the present value formula for annuities. The present value (PV) of this annuity (the $2,550,000 you could take today) equals the sum of each annual payment ($250,000) divided by (1 + r)^n, where r is the annual interest rate and n is the year of the payment. Solving for r in this equation with the given numbers, you find that the interest rate that equates the present value of the annuity to $2,550,000 is approximately 7.49%.

Suppose You Just Won the State Lottery, and You Have