Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
11th Edition
ISBN: 9780321931078
Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins
Publisher: PEARSON
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Chapter 5.2, Problem 50E
To determine
To calculate: The amount of interest of a loan
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
Chapter 5 Solutions
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Ch. 5.1 - Checkpoint 1
Find the simple interest for each...Ch. 5.1 - Checkpoint 2
For the given bonds, find the...Ch. 5.1 - Checkpoint 3
Find each future value.
(a) $1000 at...Ch. 5.1 - Checkpoint 4
You lend a friend $500. She agrees to...Ch. 5.1 - Checkpoint 5
Find the present value of the given...Ch. 5.1 - Checkpoint 6
Jerrell Davis is owned $19,500 by...Ch. 5.1 - Checkpoint 7
A firm accepts a $21,000 note due in...Ch. 5.1 - Prob. 8CPCh. 5.1 - Checkpoint 9
Find the actual interest rate paid by...Ch. 5.1 - Unless stated otherwise, "interest" means simple...
Ch. 5.1 - Find the interest on each of these loans. (See...Ch. 5.1 - Find the interest on each of these loans. (See...Ch. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Find the interest on each of these loans. (See...Ch. 5.1 - Find the interest on each of these loans. (See...Ch. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Find the interest on each of these loans. (See...Ch. 5.1 - Prob. 11ECh. 5.1 - Finance For each of the given corporate bonds,...Ch. 5.1 - Finance For each of the given corporate bonds,...Ch. 5.1 - Finance For each of the given corporate bonds,...Ch. 5.1 - Finance For each of the given corporate bonds,...Ch. 5.1 - Finance For each of the given corporate bonds,...Ch. 5.1 - Find the future value of each of these loans. (See...Ch. 5.1 - Find the future value of each of these loans. (See...Ch. 5.1 - Find the future value of each of these loans. (See...Ch. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Find the present value of each future amount. (See...Ch. 5.1 - Prob. 24ECh. 5.1 - Find the present value of each future amount. (See...Ch. 5.1 - Find the present value of each future amount. (See...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Finance Historically, treasury bills offered...Ch. 5.1 - Prob. 35ECh. 5.1 - Finance Work the following applied...Ch. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Finance Work these problems. (See Example...Ch. 5.1 - Finance Work these problems. (See Example...Ch. 5.1 - Finance Work these problems. (See Example...Ch. 5.2 - Checkpoint 1
Extend the chart in the text by...Ch. 5.2 - Checkpoint 2
Suppose $17,000 is deposited at 4%...Ch. 5.2 - Prob. 3CPCh. 5.2 - Checkpoint 4
Find the compound amount for $7500...Ch. 5.2 - Checkpoint 5
Find the face value of the zero...Ch. 5.2 - Prob. 6CPCh. 5.2 - Prob. 7CPCh. 5.2 - Prob. 8CPCh. 5.2 - Prob. 9CPCh. 5.2 - Prob. 10CPCh. 5.2 - Prob. 11CPCh. 5.2 - Interest on the zero-coupon bonds here is...Ch. 5.2 - Interest on the zero-coupon bonds here is...Ch. 5.2 - Prob. 3ECh. 5.2 - Interest on the zero-coupon bonds here is...Ch. 5.2 - Interest on the zero-coupon bonds here is...Ch. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Find the compound amount and the interest earned...Ch. 5.2 - Prob. 10ECh. 5.2 - Find the compound amount and the interest earned...Ch. 5.2 - Find the compound amount and the interest earned...Ch. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Find the interest rate (with annual compounding)...Ch. 5.2 - Prob. 20ECh. 5.2 - Find the interest rate (with annual compounding)...Ch. 5.2 - Prob. 22ECh. 5.2 - Find the compound amount and the interest earned...Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Find the compound amount and the interest earned...Ch. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Find the APY corresponding to the given nominal...Ch. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Find the present value of the given future...Ch. 5.2 - Find the present value of the given future...Ch. 5.2 - Find the present value of the given future...Ch. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Finance For Exercises 43 and 44, assume an annual...Ch. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Finance For Exercises 43 and 44, assume an annual...Ch. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - 51. Lora Reilly has inherited $10,000 from her...Ch. 5.2 - 52. Which of these 20-year zero-coupon bonds will...Ch. 5.2 - 53. As the prize in a contest, you are offered...Ch. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - 59. A company has agreed to pay $2.9 million in 5...Ch. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - 62. If inflation is 2.4% per year and a washing...Ch. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Economics Use the approach in Example 8 to find...Ch. 5.2 - Prob. 66ECh. 5.2 - 67. The consumption of electricity has increased...Ch. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.3 - Checkpoint 1
Complete these steps for an annuity...Ch. 5.3 - Prob. 2CPCh. 5.3 - Prob. 3CPCh. 5.3 - Prob. 4CPCh. 5.3 - Prob. 5CPCh. 5.3 - Checkpoint 6
(a) Ms. Black deposits $800 at the...Ch. 5.3 - Note: Unless stated otherwise, all payments are...Ch. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Find the future value of the ordinary annuities...Ch. 5.3 - Prob. 8ECh. 5.3 - Find the final amount (rounded to the nearest...Ch. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Find the final amount (rounded to the nearest...Ch. 5.3 - Find the amount of each payment to be made into a...Ch. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Find the amount of each payment to be made into a...Ch. 5.3 - Find the amount of each payment to be made into a...Ch. 5.3 - Prob. 18ECh. 5.3 - Find the interest rate needed for the sinking fund...Ch. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Find the interest rate needed for the sinking fund...Ch. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - 43. A mother opened an investment account for her...Ch. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - 47. David Horwitz needs $10,000 in 8...Ch. 5.3 - 48. Harv’s Meats knows that it must buy a new...Ch. 5.3 - 49. Barbara Margolius wants to buy a $24,000 car...Ch. 5.3 - Prob. 50ECh. 5.3 - 51. Diane Gray sells some land in Nevada. She will...Ch. 5.3 - Prob. 52ECh. 5.3 - 53. To save for retirement, Karla Harby put $300...Ch. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.4 - Prob. 1CPCh. 5.4 - Prob. 2CPCh. 5.4 - Prob. 3CPCh. 5.4 - Prob. 4CPCh. 5.4 - Prob. 5CPCh. 5.4 - Prob. 6CPCh. 5.4 - Prob. 7CPCh. 5.4 - Prob. 8CPCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Find the present value of each ordinary annuity....Ch. 5.4 - Find the present value of each ordinary annuity....Ch. 5.4 - Find the present value of each ordinary annuity....Ch. 5.4 - Find the present value of each ordinary annuity....Ch. 5.4 - Find the amount necessary to fund the given...Ch. 5.4 - Find the amount necessary to fund the given...Ch. 5.4 - Find the amount necessary to fund the given...Ch. 5.4 - Find the amount necessary to fund the given...Ch. 5.4 - Prob. 11ECh. 5.4 - Find the payment made by the ordinary annuity with...Ch. 5.4 - Prob. 13ECh. 5.4 - Find the payment made by the ordinary annuity with...Ch. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Find the payment necessary to amortize each of the...Ch. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Find the payment necessary to amortize each of the...Ch. 5.4 - Find the payment necessary to amortize each of the...Ch. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Finance Work the following applied problems.
49. A...Ch. 5.4 - Prob. 50ECh. 5.4 - Finance A student education loan has two repayment...Ch. 5.4 - Finance A student education loan has two repayment...Ch. 5.4 - Finance Use the formula for the approximate...Ch. 5.4 - Prob. 54ECh. 5.4 - Finance Use the formula for the approximate...Ch. 5.4 - 56. Mohsen Manouchehri will purchase a $230,000...Ch. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5 - Prob. 1CECh. 5 - Prob. 2CECh. 5 - Prob. 3CECh. 5 - Prob. 4CECh. 5 - Prob. 5CECh. 5 - Prob. 6CECh. 5 - Prob. 1EPCh. 5 - Prob. 2EPCh. 5 - Find the simple interest for the following...Ch. 5 - Find the simple interest for the following...Ch. 5 - Find the simple interest for the following...Ch. 5 - Find the simple interest for the following...Ch. 5 - Find the semiannual (simple) interest payment and...Ch. 5 - Prob. 6RECh. 5 - Find the maturity value for each simple interest...Ch. 5 - Find the maturity value for each simple interest...Ch. 5 - Prob. 9RECh. 5 - Find the present value of the given future...Ch. 5 - Find the present value of the given future...Ch. 5 - Prob. 12RECh. 5 - Find the present value of the given future...Ch. 5 - Find the present value of the given future...Ch. 5 - Find the compound amount and the amount of...Ch. 5 - Find the compound amount and the amount of...Ch. 5 - Find the compound amount and the amount of...Ch. 5 - Find the compound amount and the amount of...Ch. 5 - Find the amount of compound interest earned by...Ch. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Find the APY corresponding to the given nominal...Ch. 5 - Find the present value of the given amounts at the...Ch. 5 - Find the present value of the given amounts at the...Ch. 5 - Find the present value of the given amounts at the...Ch. 5 - Find the present value of the given amounts at the...Ch. 5 - Find the price that a purchaser should be willing...Ch. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Find the future value of each annuity.
33. $4000...Ch. 5 - Find the future value of each annuity.
34. $233...Ch. 5 - Find the future value of each annuity.
35. $672...Ch. 5 - Find the future value of each annuity.
36. $11,900...Ch. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Find the amount of each payment that must be made...Ch. 5 - Prob. 40RECh. 5 - Find the amount of each payment that must be made...Ch. 5 - Prob. 42RECh. 5 - Find the present value of each ordinary...Ch. 5 - Find the present value of each ordinary...Ch. 5 - Find the present value of each ordinary...Ch. 5 - Find the amount necessary to fund the given...Ch. 5 - Find the amount necessary to fund the given...Ch. 5 - Find the amount necessary to fund the given...Ch. 5 - Find the payment for the ordinary annuity with the...Ch. 5 - Find the payment for the ordinary annuity with the...Ch. 5 - Find the payment for the ordinary annuity with the...Ch. 5 - Find the payment for the ordinary annuity with the...Ch. 5 - Find the amount of the payment necessary to...Ch. 5 - Find the amount of the payment necessary to...Ch. 5 - Find the monthly house payments for the given...Ch. 5 - Prob. 56RECh. 5 - Find the monthly house payments for the given...Ch. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Prob. 60RECh. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Finance Work the following applied...Ch. 5 - Prob. 64RECh. 5 - Finance Work the following applied...Ch. 5 - Prob. 66RECh. 5 - Finance Work the following applied...Ch. 5 - Finance Work the following applied...Ch. 5 - Finance Work the following applied problems.
69. A...Ch. 5 - Finance Work the following applied...Ch. 5 - 71. In 3 years, Ms. Nguyen must pay a pledge of...Ch. 5 - 72. To finance the $15,000 cost of their kitchen...Ch. 5 - 73. To expand her business, the owner of a small...Ch. 5 - 74. The Fix family bought a house for $210,000....Ch. 5 - 75. Over a 20-year period, the class A Shares of...Ch. 5 - 76. Dan Hook deposits $400 a month to a retirement...Ch. 5 - Prob. 77RECh. 5 - 78. Eileen Gianiodis wants to retire on $75,000...
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