The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $ 1 , 800 , 000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8 % and interest is compounded semiannually.

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Answer 1

Question

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

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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…

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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, ....

Answer 2

Question

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

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Answer 3

Question

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

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Answer 4

Question

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

Expert Solution & Answer

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Answer 5

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

Answer 6

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

Answer 7

Chapter 12, Problem 18AT

(a)

To determine

To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

Answer 8

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

Answer 9

(b).

To determine

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

Answer 10

Expert Solution & Answer

Answer 11

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Answer 12

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Answer 13

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The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $ 1 , 800 , 000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8 % and interest is compounded semiannually.

Solution Summary: The author calculates the amount of sinking fund payment required by Alliance industries for a future obligation of 1,800,000.

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To calculate: The amount of sinking fund payment required to be maintained by Alliance industries for a future obligation of $1,800,000 where payment frequency is 6 months for 4 years at a nominal rate of return of 8% and interest is compounded semiannually.

To calculate: The amount by which the sinking fund payment at a nominal rate of return of 6% and interest compounded semiannually would be greater than 8% if Alliance Industries has an obligation of $1,800,000 where payment frequency is 6 months for 4 years.

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