In January of 1980, a Troy ounce of gold sold for $850 (an all-time high). Over the 28 years from 1980 to 2008, suppose the CPI has grown at a compounded annual rate of 3.3%.In 2008 a Troy ounce of gold sells for $680.
a. In real terms, with 1980 as the reference year, what is the 2008 price of gold per ounce in 1980 purchasing power?
b. If gold increases in value to keep pace with the CPI, how many years will it take to grow to $850 per ounce in 2008 purchasing power?
c. What was the real interest rate earned from 1980 to 2008 on an ounce of gold?
We have the information that
a. The real price would have been R = 680*(P/F, 3.3%, 28) = 680*(1 + 3.3%)^-28 = 273.968
b. In 2008 purchasing power, it was 680 so the time for 690 to grow to 850 is
850 = 690(F/P, 3.3%, N) or 850/690 = (1.033)^N. This gives N = ln(850/690)/ln(1.033) = 6.42 years
c. The value of gold in real terms was 273.968 and so the required rate of return is
273.968 = 850*(1 + i%)^28
(273.968/850)^(1/28) - 1 = -3.693%
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