Asked by Michael Mocan on May 01, 2024
Verified
Assume that you have just won $5,000,000 in the lottery and will receive $250,000 per year for the next 20 years. How much is your prize worth today if the interest rate is 8%?
A) $1,072,731
B) $2,454,525
C) $2,185,219
D) $1,165,250
Lump Sum
A large single payment of money instead of a series of smaller payments or installments.
Annual Payments
Regular payments made once a year, often associated with loans, annuities, or other financial agreements.
Interest Rate
It's the rate, in the form of a percentage of the principal, charged by lenders to borrowers for asset usage.
- Become familiar with the idea of present value and its relationship with interest rate adjustments and temporal factors.
- Assess the financial value of contracts or lottery winnings when presented as an annuity versus a lump sum.
Verified Answer
ZK
Zybrea KnightMay 03, 2024
Final Answer :
B
Explanation :
The prize's present value can be calculated using the formula for the present value of an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods. Plugging in the values ($250,000 for P, 0.08 for r, and 20 for n), the calculation gives a present value of approximately $2,454,525, making option B the correct answer.
Learning Objectives
- Become familiar with the idea of present value and its relationship with interest rate adjustments and temporal factors.
- Assess the financial value of contracts or lottery winnings when presented as an annuity versus a lump sum.