For question 1 parts a,b,c below, show all work that justifies your results. You will show how to use series to compare values of payments over time with a lump sum payment today. The value of future payments in terms of today's dollars is known as the present value of those payments. 1. a. What is the present value formula if annual payments of C dollars continue indefinitely, assuming an average annual interest rate r? Write the answer as a series using summation notation b. Rewrite the summation formula found in part a. as a geometric series, and then find the sum. The answer will be a fraction containing C and r. c. For annuities with a present value of $1 million, calculate the annual payouts given over 25 years assuming interest rates of 1%, 5%, and 10%. Use the formula you obtained in part b. There are three answers- one for each rate, measured in dollars. Round each answer to the nearest cent.

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
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For question 1 parts a,b,c below, show all work that justifies your results. You will show how to
use series to compare values of payments over time with a lump sum payment today. The value
of future payments in terms of today's dollars is known as the present value of those payments.
1. a. What is the present value formula if annual payments of C dollars continue indefinitely,
assuming an average annual interest rate r? Write the answer as a series using
summation notation
b. Rewrite the summation formula found in part a. as a geometric series, and then find
the sum. The answer will be a fraction containing C and r.
c. For annuities with a present value of $1 million, calculate the annual payouts given
over 25 years assuming interest rates of 1%, 5%, and 10%. Use the formula you
obtained in part b. There are three answers- one for each rate, measured in dollars.
Round each answer to the nearest cent.
Transcribed Image Text:For question 1 parts a,b,c below, show all work that justifies your results. You will show how to use series to compare values of payments over time with a lump sum payment today. The value of future payments in terms of today's dollars is known as the present value of those payments. 1. a. What is the present value formula if annual payments of C dollars continue indefinitely, assuming an average annual interest rate r? Write the answer as a series using summation notation b. Rewrite the summation formula found in part a. as a geometric series, and then find the sum. The answer will be a fraction containing C and r. c. For annuities with a present value of $1 million, calculate the annual payouts given over 25 years assuming interest rates of 1%, 5%, and 10%. Use the formula you obtained in part b. There are three answers- one for each rate, measured in dollars. Round each answer to the nearest cent.
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