Question

A coin sold at auction in 2017 for $8.406,000. The coin had a face value of $15 When was issued in 1787 and had previously been sold for $265.000 in 1975. wwwAt what annual rate did the coin appreciate from its first minting to the 1975 sale (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g. 32.16.) What annual rate did the 1975 buyer earn on his purchase? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 52.16.) At what annual rate did the coin appreciate from its first minting to the 2017 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g.. 32.16.) Rate of return from 1787 to 1975 Rate of return from 1975 to 2017 c. Rate of return from 1787 to 2017

Answer 1

Answer to Question 1:

Part a:

Rate of Return = (Value of Coin in 1975 / Value of Coin in 1787)^(1/188) - 1
Rate of Return = ($265,000 / $15)^(1/188) - 1
Rate of Return = 17,666.6667^(1/188) - 1
Rate of Return = 1.0534 - 1
Rate of Return = 0.0534 or 5.34%

Part b:

Rate of Return = (Value of Coin in 2017 / Value of Coin in 1975)^(1/42) - 1
Rate of Return = ($8,406,000 / $265,000)^(1/42) - 1
Rate of Return = 31.72075^(1/42) - 1
Rate of Return = 1.0858 - 1
Rate of Return = 0.0858 or 8.58%

Part c:

Rate of Return = (Value of Coin in 2017 / Value of Coin in 1787)^(1/230) - 1
Rate of Return = ($8,406,000 / $15)^(1/230) - 1
Rate of Return = 560,400^(1/230) - 1
Rate of Return = 1.0592 - 1
Rate of Return = 0.0592 or 5.92%