A coin sold at auction in 2017 for $4,120,500. The coin had a face value of $20

Question

A coin sold at auction in 2017 for $4,120,500. The coin had a face value of $20 when it was issued in 1786 and had previously been sold for $395,000 in 1968.

At what annual rate did the coin appreciate from its first minting to the 1968 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

A coin sold at auction in 2017 for $4,120,500. The coin had a face value of $20 when it was issued in 1786 and had previously been sold for $395,000 in 1968.

Explanation / Answer

These questions require application of basic time value of money function, which is FV = PV * (1 + r)n.

Part a) 395,000 = 20 * (1 + r)100

19,750 = (1 + r)100

1.1040 = 1 + r

r = 10.40%

Part b) 4,120,500 = 395,000 * (1 + r)49

10.4316 = (1 + r)49

1.0490 = 1 + r

r = 4.90%

Part c) 4120500 = 20 * (1 + r)149

206025 = (1 + r)149

1.0856 = 1 + r

r = 8.56%

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