Question

a. A coin sold at auction in 2017 for $2,897,000. The coin had a face value of $10 when it was issued in 1795 and had previously been sold for $310,000 in 1970. At what annual rate did the coin appreciate from its first minting to the 1970 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What annual rate did the 1970 buyer earn on his purchase? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) 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.) C. a. Rate of return from 1795 to 1970 b. Rate of return from 1970 to 2017 c. Rate of return from 1795 to 2017 % % %

Answer 1

Part a:

Rate of Return = (Value of Coin in 1970 / Value of Coin in 1795)^(1/175) - 1
Rate of Return = ($310,000 / $10)^(1/175) - 1
Rate of Return = $31,000 ^(1/175) - 1
Rate of Return = 1.0609 - 1
Rate of Return = 0.0609 or 6.09%

Part b:

Rate of Return = (Value of Coin in 2017 / Value of Coin in 1970)^(1/47) - 1
Rate of Return = ($2,897,000 / $310,000)^(1/47) - 1
Rate of Return = 9.3452^(1/47) - 1
Rate of Return = 1.0487 - 1
Rate of Return = 0.0487 or 4.87%

Part c:

Rate of Return = (Value of Coin in 2017 / Value of Coin in 1795)^(1/222) - 1
Rate of Return = ($2,897,000 / $10)^(1/222) - 1
Rate of Return = 289700^(1/222) - 1
Rate of Return = 1.0583 - 1
Rate of Return = 0.0583 or 5.83%