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Question 1 Historic Redstone Castle is for sale A castle built for the man who founded the town of Redstone, CO, can now be yours, for $19.75 million. (Sherman, T.) A coal magnate, John Cleveland Osgood, built the castle for his wife near the town of Redstone, which was founded as a company town for people working in the coal mining industry. Construction began in 1897 and was completed in 1902. (Sherman, T.) In the early 1900s, John Cleveland Osgood was known as the King of Coal in the West. He was sixth richest of the Robber Barons, a group of elite industrialists. As a social and industrial experiment, Osgood decided he wanted to build a town in the Colorado mountains that would provide better living conditions for the miners working nearby. Instead of the tents and tiny cabins common in mining towns, Osgood built Swiss-style cottages – with electricity and running water - along the river. He also built a clubhouse with a theater, school, library, lodge, community garden and stables. (Kesting, A.). Known as Redstone Castle and as the "Ruby of the Rockies," the 42-room castle has almost 30,000 square feet of interior space. It also has over 150 acres of land, surrounded by beautiful scenery along the Crystal River. (Sherman, T.) It's not the first time the castle has been up for sale in recent years. Steve and April Carver purchased it at an auction for $2.2 million in 2016. (Oravetz, J.) The Carvers worked to renovate and restore the castle and have operated it as a hotel since 2018. (Oravetz, J.) It features nine restored boutique suites, where dignitaries such as Teddy Roosevelt and the Rockefellers once slept. It was also open to the public for guided tours on weekends and was available to host weddings and other private events. (Oravetz, J.)   References Sherman, T. (2020, Sep 23). Historic Colorado Castle in the Rockies Can Be Yours—Antique Ski Lift Included, from https://www.realtor.com/news/unique-homes/historic-colorado-castle-antique-ski-lift-included/ Kesting, Amanda (2019, February 22). You can spend the night in a 117-year-old castle in this tiny Colorado mountain town, from  https://www.9news.com/article/life/style/colorado-guide/you-can-spend-the-night-in-a-117-year-old-castle-in-this-tiny-colorado-mountain-town/73-3dc8bd41-828a-4a0d-8f79-61d15614e4cb Oravetz, Janet. (2020, September 16). Historic Redstone Castle for sale once again, from https://www.realtor.com/news/unique-homes/general-robert-e-lees-boyhood-home-sale/ ****************************************************************** In your initial response to the topic you have to answer all questions. 1. Calculate the annual compound growth rate of the Redstone Castle price since the house was purchased by Steve and April Carver (in 2016) until it was listed for sale in 2020. (The growth rate should be calculated to two decimals in percentage form. Round the number of years to the whole number). Please show your work. 2. Assume that the average compound growth rate prevailed since John Cleveland Osgood built the Castle in 1902 until 2016 was 5.52% per year compounded annually. Calculate the price of the house in 1902. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work. 3. You were using the time value of money concept to answer question #2. Think about the timeline for that problem. What year is considered as the time point 0 in that problem? Please explain your answer  4. Assume that the average compound growth rate you were using in the question #2 now is compounded daily. Calculate the price of the house in 1902. Compare with your answer to the question #2.  (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.  5. Assume that the house was purchased for the price listed in 2020. A commercial bank loaned the buyer the whole price (zero down payment) for 30 years. The loan must be repaid in equal monthly payments at the end of the month. The annual interest rate on the loan is 3.45% of the unpaid balance. What is the amount of the monthly payments? Please show your work.   6. Reflection – the students also should include a paragraph in the initial response in their own words reflecting on specifically what they learned from the assignment and how they think they could apply what they learned in the workplace or in everyday life.
Answered 3 days AfterMay 26, 2022

Answer To: see attach

Prateek answered on May 30 2022
102 Votes
1. To determine the compounded annual growth rate, we need to first identify the number of years for which the rate is to be determined which is a period from 2016 to 2020 (4 years of growth). The price in 2016 was $2.2 million and in 2020 is to be sold for $19.75 million. By using the formula for CAGR, the computed rate is 73.10%.
The calculation for the same is shown below:
CAGR = (Current Price/ Previous Price)^ (1/n) - 1
CAGR = (19.75/2.2)^(1/4) – 1
CAGR = 73.10%
2. The price is 1902 can be determined using the CAGR of 5.52% which is compounded annually. Since there is a period 114 years between the two dates, we can use the same CAGR formula as used in Question 1 by solving for the previous price (which will be the price in 1902). The computed price in 1902 for the villa is estimated to be $4,811.24. The computation for the same is shown as follows:
CAGR = (Current Price/ Previous Price)^ (1/n) – 1
5.52% = ($2,200,000/PP)^(1/114)-1
PP = $4,811.24
This calculation can be done easily on excel or using a calculator.
3. Since the overall CAGR from 1902 to 2016 was 5.52%. We can take the number of years in the middle of these two years to determine the number of years used to compute the value of the villa in 1902. Just subtract 2016 from 1902 to determine the number of years, which is 114 in this case. Thus, at time 0, the 1902 is the year which is considered.
4. If the CAGR is compounded daily, then we have to divide the CAGR by 365 and multiply the number of years by 365 in the solution to Question 2. Thus, the rate used will be 0.015123% and the number of periods will be 41,610. The computed price of the villa in 1902 will then be $4,070.99. The calculations for the same are given as follows:
CAGR = (Current Price/ Previous Price)^ (1/n) – 1
0.015123% = ($2,200,000/PP)^(1/41,610)-1
PP = $4,070.99
Further, it makes sense that the price of the villa has dropped now because the rate is now being compounded daily and the number of period have increased. Moreover, the price is being compounded on a daily basis rather than annually. This makes the present value in 1902 cheaper.
5. To determine the monthly payment (PMT) for the loan, one needs to determine 4 variables:
a. Number of periods (n)
b. Rate (r)
c. Present Value (PV)
d. Future Value (FV)
The number of periods will be computed by multiplying the loan period of 30 years by 12, which is 360. The rate will be determined by dividing the annual interest rate of 3.45% by 12, which is 0.2875%. The present value will be the value of the loan, which is the price of the villa in this case, which is $19.75 million. The future value will be zero because the loan will be paid off by then....
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