I recently found a real-life advertisement in the newspaper. (Only the phone number has been changed.) Suppose that you have won a $10,000,000 lottery, paid in 20 annual installments. How much would be a fair price to be paid today for the assignment of this prize? Assume the money could be invested at 11%. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)
P*1.11^20 = 10000000
P = 10000000/1.11^20 ≈ 1.24 million
I recently found a real-life advertisement in the newspaper. (Only the phone number has been changed.) Suppose that you have won a $10,000,000 lottery, paid in 20 annual installments. How much would be a fair price to be paid today for the assignment of this prize? Assume the money could be invested at 10%. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)
Well, if you won $10,000,000 in the lottery, the fair price to be paid today for the assignment of this prize would be... an overwhelming sense of gratitude and excitement! Let's face it, money can't buy happiness, but it certainly can make for some interesting shopping sprees! As for investment advice, you could consider investing in a solid supply of watermelons or clown shoes. That's an investment plan bound to bring joy and laughter to both your heart and your bank account!
To determine the fair price to be paid today for the assignment of the prize, we need to calculate the present value of the annuity payments.
Given:
- Prize amount: $10,000,000
- Number of annual installments: 20
- Interest rate: 11%
To calculate the present value, we can use the formula for the present value of an ordinary annuity:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Annual payment
r = Interest rate per period
n = Number of periods
In this case, the annual payment is $10,000,000 / 20 = $500,000.
Plugging in the values into the formula:
PV = $500,000 × [(1 - (1 + 0.11)^(-20)) / 0.11]
Calculating the present value:
PV = $500,000 × [(1 - (1.11)^(-20)) / 0.11]
PV = $500,000 × [(1 - 0.1296) / 0.11]
PV = $500,000 × (0.8704 / 0.11)
PV = $500,000 × 7.9136
PV = $3,956,800
Therefore, a fair price to be paid today for the assignment of this prize would be approximately $3,956,800.
To determine the fair price to be paid today for the assignment of the $10,000,000 lottery prize, we need to calculate the present value of the 20 annual installments. This can be achieved by discounting each future cash flow back to the present at the given interest rate of 11%.
The formula to calculate the present value of an ordinary annuity is given as:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
C = Cash flow per period (annual installment payment)
r = Interest rate per period (11% or 0.11 in decimal form)
n = Number of periods (20 annual installments)
In this case, C is the annual installment payment, which can be calculated by dividing the total prize amount ($10,000,000) by the number of installments (20).
C = $10,000,000 / 20 = $500,000
Using the given values, we can plug them into the formula to calculate the present value (fair price) of the lottery prize:
PV = $500,000 * (1 - (1 + 0.11)^(-20)) / 0.11
Calculating this equation will give us the fair price to be paid today for the assignment of the prize. Let's perform the calculation:
PV = $500,000 * (1 - (1.11)^(-20)) / 0.11
PV ≈ $4,494,823.65
Therefore, the fair price to be paid today for the assignment of the $10,000,000 lottery prize, assuming an interest rate of 11% and paid in 20 annual installments, would be approximately $4,494,823.65 (rounded to the nearest cent).