Question

The Hamptons Home of a Famed Socialite Hits the Market "Before there was Paris Hilton, there was Consuelo Vanderbilt Balsan -a Gilded Age heiress and socialite, renowned for her beauty and wealth. Ms. Balsan's onetime Hamptons home was slated to hit the market priced at $38 million with Tim Davis of the Corcoran Group. Located on Ox Pasture Road in Southampton, the shingle-style home was built around 1910 and is known as "Gardenside" or "Cara-Mia". Ms. Balsan, the great-granddaughter of railroad magnate Cornelius Vanderbilt, owned the house until her death in 1954. According to public records, the estate is owned by Robert G. Goldstein, executive vice president and president of global gaming operations at Las Vegas Sands Corp, and his wife Sheryl, who purchased the house in 2002 for $17.4 million." (The Wall Street Journal, August 1, 2014, M2) In your initial response to the topic you have to answer all questions. You are expected to make your own contribution in a main topic as well as respond with value added comments to at least two of your classmates as well as to your instructor. 1. Calculate the annual compound growth rate of the house price during the period when the house was owned by Robert G. Goldstein (since 2002). (Round the number of years to the whole number). Please show your work. 2. Assume that the growth rate you calculated in question #1 remains the same for the next 30 years. Calculate the price of the house in 30 years after it was sold by Robert G. Goldstein. Please show your work. 3. Assume that the growth rte you calculated in question #1 remains the same since the house was sold. Calculate the price of the house today. (Round the number of years to the whole number). Please show your work

Answer 1

Answer 1. Over the course of 12 years from 2002 to 2014 your investment grew from $17.4 million to $38 million. Its compound annual growth rate (CAGR) is 6.73 %.

The formula for CAGR is:

CAGR = ( FV / SV )^{1 / N} - 1

where:

FV = final value of an investment
SV = starting value of an investment
N = total number of investment periods in years

Answer 2 : The price of the house will be $268,150,665.66 after 30 years if CAGR will be 6.73 %

Breakdown Balance Accumulation Graph S300.0M 14% -Principal Interest Balance $200.0M 86% S100.0M Starting Amount Interest $0 10yr 15yr 20yr 25yr 30yi Oyr Syr

Answer 3 : The price of the house will be $52,627,912.48 after 5 years (2014 - 2019) if CAGR will be 6.73 %