A coin that was featured in a famous novel sold at auction in 2014 for $3,450,50

Question

A coin that was featured in a famous novel sold at auction in 2014 for $3,450,500. The coin had a face value of $1 when it was issued in 1792 and had previously been sold for $385,000 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.

- What annual rate did the 1973 buyer earn on his purchase? (Show working as well please) Thanks

- What annual rate did the 1973 buyer earn on his purchase? (Show working as well please) Thanks

Explanation / Answer

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

a.

385000=1(1+r/100)^181

(385000/1)^(1/181)=(1+r/100)

(1+r/100)=1.0736

r=(1.0736-1)*100

=7.36%(Approx).

b.

3,450,500=385000(1+r/100)^41

(3,450,500/385000)^(1/41)=(1+r/100)

(1+r/100)=1.05494

r=(1.05494-1)*100

=5.49%(Approx).

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