Question

A coin that was featured in a famous novel sold at auction in 2014 for $2,654,800. The coin had a face value of $2 when it was issued in 1793 and had previously been sold for $380,000 in 1972. At what annual rate did the coin appreciate from its first minting to the 1972 sale? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return % What annual rate did the 1972 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.) Rate of return % 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

Answer 1

1

Future value = present value*(1+ rate)^time

380000 = 2*(1+Interest rate/100)^179

Interest rate % = 7.03

Using Calculator: press buttons "2ND"+"FV" then assign

FV =380000

PV =-2

N =179

PMT = 0

CPT I/Y

Using Excel

=RATE(nper,pmt,pv,fv,type,guess)

=RATE(Interest rate/100,,-2,380000,,)

2

Future value = present value*(1+ rate)^time

2654800 = 380000*(1+Interest rate/100)^42

Interest rate % = 4.74

Using Calculator: press buttons "2ND"+"FV" then assign

FV =2654800

PV =-380000

N =42

PMT = 0

CPT I/Y

Using Excel

=RATE(nper,pmt,pv,fv,type,guess)

=RATE(Interest rate/100,,-380000,2654800,,)

3

Future value = present value*(1+ rate)^time

2654800 = 2*(1+Interest rate/100)^221

Interest rate % = 6.59

Using Calculator: press buttons "2ND"+"FV" then assign

FV =2654800

PV =-2

N =221

PMT = 0

CPT I/Y

Using Excel

=RATE(nper,pmt,pv,fv,type,guess)

=RATE(Interest rate/100,,-2,2654800,,)