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Calculating Rates of Return [LO3] A coin sold at auction in 2017 for $2,897,000. The coin...

Calculating Rates of Return [LO3]

A coin sold at auction in 2017 for $2,897,000. The coin had a face value of $10 when it was issued in 1795 and had previously been sold for $310,000 in 1970.

  

a.

At what annual rate did the coin appreciate from its first minting to the 1970 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. What annual rate did the 1970 buyer earn on his purchase? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c. At what annual rate did the coin appreciate from its first minting to the 2017 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Solutions

Expert Solution

Part a
Annual Rate formula = ((Final value/Initial Value)^(1/number of years)) -1 *100
Value of coin in 1795 = $10
Value of coin in 1970 = $310,000
Numbers of years from 1795 to 1970 = 1970-1795 = 175
Annual Rate = ((310,000/10)^1/175)) -1 *100
Annual rate = 6.087673%
Annual rate = 6.09% approx
Part b
The buyer has bought the coin for $310,000 when the coin was minted in 1795. He is selling the coin for $2,897,000 in 2017.
Annual Rate formula = ((Final value/Initial Value)^(1/number of years)) -1 *100
Value of coin in 1970 = $310,000
Value of coin in 2017 = $2,897,000
Numbers of years from 1970 to 2017 = 2017-1970 = 47
Annual Rate = ((2,897,000/310,000\)^1/175)) -1 *100
Annual rate = 4.869883%
Annual rate = 4.87% approx
Part c
The coin appreciated from $10 in 1795 to $ 2,897,000 in 2017
Annual Rate formula = ((Final value/Initial Value)^(1/number of years)) -1 *100
Value of coin in 1795 = $10
Value of coin in 2017 = $2,897,000
Numbers of years from 1795 to 2017 = 2017-1795 = 222
Annual Rate = ((2,897,000/10)^1/222)) -1 *100
Annual rate = 5.828678%
Annual rate = 5.83% approx

jeff jeffy answered 1 year ago
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