After winning the lottery,you state that you are indifferent between receiving twenty $500,000 end-of-the-year payments (first payment one year from today),or a lump sum of $5,297,007 today.What interest rate are you using in your decision-making process such that you are indifferent between the two choices?
A)5.00%
B)6.00%
C)7.00%
D)8.00%

Question

Quizplus · Accepted Answer

This is a problem of calculating the present value of an annuity. The formula to calculate the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the number of periods. In this case, we are given the present value ($5,297,007), the payment per period ($500,000), and the number of periods (20 years). We need to find the interest rate (r) that makes the present value of the annuity equal to the lump sum offered today.By substituting the given values into the formula and solving for r, or by using a financial calculator or spreadsheet to solve for the interest rate that equates the present value of the annuity payments to the lump sum offered, we find that the interest rate is approximately 7%. This means that at a 7% interest rate, the present value of the twenty $500,000 end-of-the-year payments is equal to receiving $5,297,007 today, making the individual indifferent between the two choices.

After Winning the Lottery,you State That You Are Indifferent Between