Question 3 (25 points): If the present value of a perpetuity is given by:where C is the periodic payments and r is the discount rate. Show that the present value of anannuity of n years is given by:1C - (1 + r)]

The present value of the annuity helps you understand what a lump sum of money today would be worth…

Answered: Question 3 (25 points): If the present…

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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1
To find the present value (PV) of an ordinary annuity, a. the interest is compounded and then subtracted from the FV. O b. each payment is divided by (1+1)* c. each payment is multiplied by (1+1). O d. the future value (FV) is divided by the interest rate. e. the future value is divided by (1+1)*:
To determine the converted table factor for the present value of an annuity due, one must find the factor for the present value of an ordinary annuity for n + 1 and then add 1. n − 1 and then subtract 1. n − 1 and then add 1. n + 1 and then subtract 1.
In the time diagram below, which of the following concepts is depicted? 0 PV $1 2 $1 3 $1 O Present value of an annuity due O Future value of an ordinary annuity Present value of an ordinary annuity Future value of an annuity due 4 $1
Calculate the future value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) 1. 2. 3. Annuity Annual Payment Rate $4,700 6.0 % 8.0 % 7,700 6,700 10.0 % Show Transcribed Text 1. 2. 3. Annuity Annual Payment Rate Interest Compounded Quarterly Annually Semiannually $ 5,700 Interest Compounded 8.0 % Quarterly 10,700 11.0% Annually 4,700 10.0 % Semiannually Period Invested 5 years 6 years 9 years Calculate the present value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) $ Period Invested 2 years 5 years 3 years Future Value of Annuity 172,892.28 Present Value of Annuity
Which of the following is the formula for the future value of an annuity? Multiple choice question. FVA = C ((1+r)t–1r)(1+r)t–1r FVA = C (1−1(1+r)tr)1-1(1+r)tr FVA = C ((1–r)t+1r)
Which of following formulas is used to calculate the present value of a perpetual annuity? Seleccione una: a. P= f / (1+i)^n b. P= f / (i - g) c. P= a / (i - g) d. P= a / (1+i)^n e. F = P * (1+i)^n
Rank the following from highest present value to lowest present value. Assume all else equal. v An annuity with 10 payments v An annuity due with 15 payments v A perpetuity v An annuity with 15 payments
15.
The formula 1/(1 + r)t is used to calculate Multiple Choice The present value annuity factor. The present value interest factor. The future value interest factor. The present value of $1 occurring t periods from now.
Calculate the future value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) Annuity Payment Annual Rate Interest Compounded Period Invested Future Value of Annuity 1. $3,100 8.0 % Semiannually 9 years $79,500.77 2. 6,100 10.0 % Quarterly 5 years 3. 5,100 12.0 % Annually 6 years
kk.

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Question 3 (25 points): If the present value of a perpetuity is given by: where C is the periodic payments and r is the discount rate. Show that the present value of an annuity of n years is given by: 1 C - (1 + r)]