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…

Financial And Managerial Accounting

15th Edition

ISBN:9781337902663

Author:WARREN, Carl S.

Publisher:WARREN, Carl S.

Chapter11: Liabilities: Bonds Payable

Section: Chapter Questions

Problem 11E

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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)
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
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.
The ___________ of an annuity is the amount that must be invested now at interest rate i per time period to provide n payments each of amount R.
Use a calculator to evaluate the present value of an annuity formula 1-(1+ 4) -nt P = m for the values of the variables m, r, and t (respectively). Assumen= 12. (Round your answer to the nearest cent.) $50; 5%; 7 yr %24
Task: Assume that at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount x, is due at the end of the rth year. Let the effective annual interest rate for the rth year be i,. Give an identity which expresses L in terms of the x, and i,. Answer: The identity is [ Select ] [ Select ] L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-2) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-2) ... (1+i_n)^(-n) L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2) + ... + x_n (1+i_1) (1+i_2) ... (1+i_n) L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-1) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-1) ... (1+i_n)^(-1) Question 3 L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2)^2 + ... + x_n (1+i_1) (1+i_2)^2 ... (1+i_n)^n
Multiple Choice Question Which of the following is the formula for the present value of a growing annuity? (C is the payment to occur at the end of the first period, r is the interest rate, g is the rate of growth per period expressed as a percentage, and t is the number of periods for the annuity.) Multiple choice question. PV = C(r−g)C(r−g) (1−((1−g)(1−r))t)1−(1-g)(1-r)t PV = C(r−g)C(r−g) (1−((1+g)(1+r))t)1−(1+g)(1+r)t PV = C(r−g)C(r−g) (1−((1−g)(1+r))t)1−(1-g)(1+r)t PV = C(r−g)C(r−g) (1−((1+g)(1−r))t)
Cc. 174.
Q. 4
An [Select] is a sequence of equal period payments. If payments are made at the end of each time interval, the annuity is called an [Select]
4. The present value of a growing perpetuity, with cash flow C1 occurring one year from now, is given by: [C1/(r - g)], where r > g. True or False ? 5. An equal-payment home mortgage is an example of an annuity. True or False?

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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)]