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.)
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.

The annual compound growth rate of the Redstone Castle price is 73.10%.

From the information given, the formula to calculate the annual compound growth rate will be:

g = (F/P)^(1/n) - 1

where g = growth rate

f = final value = 19750000

p = initial value = 2200000

n = period = 2020 - 2016 = 4

g = (F/P)^(1/n) - 1

g = (19750000/2200000)^(1/4) - 1

g = 73.10%

Therefore, the growth rate is 73.10%

The price of the house in 1902 will be calculated thus:

PV = F/(1 + g)^n

= 19750000/(1 + 73.10%)^4

= $4811

The year that is considered as the time point 0 in that problem is 1902.

When the average compound growth rate in the question #2 now is compounded daily, the price of the house in 1902 will be $4071. The difference in values will be:

= $4811 - $4071

= $740

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