How much are the 2 million dollars received annually over the course of 25 years worth in terms of today's dollars, assuming an annual interest rate of 4%?
How much are the 2 million dollars received annually over the course of 25 years worth in terms of today's dollars, assuming an annual interest rate of 4%?
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
Related questions
Question
Answer for part d and e only.
![1. Suppose you win the lottery and are given the following three options: (1) Receive 30 million dollars today; (2) receive
2 million dollars per year over the next 25 years; or (3) receive 1 million dollars per year indefinitely (being passed on to
your heirs). Which is the best deal, assuming that the annual interest rate is 4%? We answer this by working through the
following sequence of questions.
a. How much are the 2 million dollars received annually over the course of 25 years worth in terms of today's dollars,
assuming an annual interest rate of 4%?
b. Use the answer to part a. to find a general formula for the present value of payments of C dollars received each year
over the next n years, assuming an average annual interest rate r.
c. Find a formula for the present value if annual payments of C dollars continue indefinitely, assuming an average
annual interest rate r.
d. Use the answer to part c. to determine the present value of 1 million dollars paid annually indefinitely.
e. Use your answers to parts a. and d. to determine which of the three options is best.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95ba2087-e8f0-410b-96a8-451d77315e1b%2Fbe23f9cb-9373-4c01-96bb-d8dfe8eaef73%2Fqco0tvg_processed.png&w=3840&q=75)
Transcribed Image Text:1. Suppose you win the lottery and are given the following three options: (1) Receive 30 million dollars today; (2) receive
2 million dollars per year over the next 25 years; or (3) receive 1 million dollars per year indefinitely (being passed on to
your heirs). Which is the best deal, assuming that the annual interest rate is 4%? We answer this by working through the
following sequence of questions.
a. How much are the 2 million dollars received annually over the course of 25 years worth in terms of today's dollars,
assuming an annual interest rate of 4%?
b. Use the answer to part a. to find a general formula for the present value of payments of C dollars received each year
over the next n years, assuming an average annual interest rate r.
c. Find a formula for the present value if annual payments of C dollars continue indefinitely, assuming an average
annual interest rate r.
d. Use the answer to part c. to determine the present value of 1 million dollars paid annually indefinitely.
e. Use your answers to parts a. and d. to determine which of the three options is best.
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