A coin that was featured in a novel sold at auction in 2014 for $2, 591, 000. Th

Question

A coin that was featured in a novel sold at auction in 2014 for $2, 591, 000. The coin had a face value of $5 when it was issued in 1785 and had previously been sold for $165, 000 in 1973. At what annual rate did the coin appreciate from its first minting to the 1973 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 1973 buyer earn 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. FV = PV *(1+r)^n where FV = 165,000 PV = 5 and n= 1973-1785 = 188 years and r= ?

165,000 = 5 *(1+r)^188

165000/5 = (1+r)^188

33000=(1+r)^188

(1+r) = 33000^(1/188) = 1.05690

r = rate of return =0.0569 = 5.69%

b. FV = PV *(1+r)^n where FV = 2,591,000 PV = 165,000 and n= 2014-1973 = 41 years and r= ?

2,591,000 =165,000*(1+r)^41

1+r = (2,591,000/165,000)^(1/41)

1+r =1.06947

r = rate of return = 0.06947 = 6.95%

c. FV = PV *(1+r)^n where FV = 2,591,000 PV = 5 and n= 2014-1785 = 229 years and r= ?

2,591,000 = 5*(1+r)^229

1+r = (2,591,000/5)^(1/229)

1+r = 1.05914

r = rate of return = 0.05914 = 5.91%

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