A coin that was featured in a famous novel sold at auction in 2014 for $6.788.00

Question

A coin that was featured in a famous novel sold at auction in 2014 for $6.788.000. The coin had a face value of $5 when it was issued in 1790 and had previously been sold for $280.000 in 1967. At what annual rate did the coin appreciate from its first minting to the 1967 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 1967 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.)

Explanation / Answer

a) Present value $5 FV $280,000 Number of years = 1967 - 1790 + 1 178 FV = PV x (1+r)^n 280000 = 5 x (1+r)^178 280000 / 5 = (1+r)^178 56000 ^(1/178) = 1+r 1.0633 - 1 = r = 6.33% b) Present value $    280,000 FV $ 6,788,000 Number of years = 2014 - 1967 + 1 48 FV = PV x (1+r)^n 6788000 = 280000 x (1+r)^48 6788000 / 280000 = (1+r)^48 24.24 ^(1/48) = 1+r 1.0687 - 1 = r = 6.87% c) Present value $5 FV $ 6,788,000 Number of years = 2014 - 1790 + 1 225 FV = PV x (1+r)^n 6788000 = 5 x (1+r)^225 6788000 / 5 = (1+r)^225 1357600 ^(1/225) = 1+r 1.0648 - 1 = r = 6.48%

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