Present Value of an Annuity On January 1, you win $2,900,000 in the state lottery. The $2,900,000 prize will be paid in equal installments of $290,000 over 10 years. The payments will be made on December 31 of each year, beginning on December 31 of the current year. If the current interest rate is 6%, determine the present value of your winnings. Use present value table. Round o the nearest whole dollar. $
Present Value of an Annuity On January 1, you win $2,900,000 in the state lottery. The $2,900,000 prize will be paid in equal installments of $290,000 over 10 years. The payments will be made on December 31 of each year, beginning on December 31 of the current year. If the current interest rate is 6%, determine the present value of your winnings. Use present value table. Round o the nearest whole dollar. $
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
. **Round to the nearest whole dollar.**
### Calculation:
The formula for calculating the present value of an annuity is:
\[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r \]
Where:
- \( PV \) is the present value of the annuity
- \( PMT \) is the annual payment ($290,000)
- \( r \) is the annual interest rate (6% or 0.06)
- \( n \) is the number of years (10 years)
Use the present value table to find the factor corresponding to an annual interest rate of 6% for 10 years and multiply it by the annual payment of $290,000. Round the final answer to the nearest whole dollar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d7bc6d0-51a6-4309-ba9c-2be68c6aa30f%2Fb05a6b43-b265-4433-8966-20b0e226e82f%2F91p6e0t_processed.png&w=3840&q=75)
Transcribed Image Text:### Present Value of an Annuity
#### Problem Statement:
On January 1, you win $2,900,000 in the state lottery. The $2,900,000 prize will be paid in equal installments of $290,000 over 10 years. The payments will be made on December 31 of each year, beginning on December 31 of the current year. If the current interest rate is 6%, determine the present value of your winnings. Use the [present value table](#). **Round to the nearest whole dollar.**
### Calculation:
The formula for calculating the present value of an annuity is:
\[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r \]
Where:
- \( PV \) is the present value of the annuity
- \( PMT \) is the annual payment ($290,000)
- \( r \) is the annual interest rate (6% or 0.06)
- \( n \) is the number of years (10 years)
Use the present value table to find the factor corresponding to an annual interest rate of 6% for 10 years and multiply it by the annual payment of $290,000. Round the final answer to the nearest whole dollar.
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