Question

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?

Answer 1

We have the information that

• In January of​ 1980, price of gold was​ $850. From 1980 to 2008, CPI has grown at a compounded annual rate of 3.3​%.
• In 2008 the price was $680.

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%