A coin that was featured in a famous novel sold at auction in 2014 for $6,794,00

Question

A coin that was featured in a famous novel sold at auction in 2014 for $6,794,000. The coin had a face value of $1 when it was issued in 1794 and had previously been sold for $215,000 in 1971.

At what annual rate did the coin appreciate from its first minting to the 1971 sale? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What annual rate did the 1971 buyer earn on his purchase? (Do not round intermediate calculations. 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 2014 sale? (Do not round intermediate calculations. 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 1971 sale? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation / Answer

future value = previous value * (1+ rate of return)^number of years

=>
a)

215000 = 1 * (1 + r%)^177

=>
rate of return r = 7.18%

b)

6794000 = 215000 ( 1+r)^43

=>
rate of return = 8.36%

c)

6794000 = 1 * ( 1 + r%)^220

rate of return r% = 7.41%

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