You are trying to estimate the real interest rate for the mining industry produc

Question

You are trying to estimate the real interest rate for the mining industry products and proceed as follows. You consider buying coal and gold in equal proportion of today's dollars, spending $1000 on coal, and another $1000 on gold. In 7 years from now, the selling values in actual dollars are predicted to be $1286 (coal) and $1288 (gold). Inflation (for coal) is 1.6% per year, for the next 7 years. For gold, the gold price index is predicted to rise in the next 7 years from the current 414 points to 438 points. Compute the estimated real interest rate, as a number, with 0.001 precision.

Explanation / Answer

Purchase Price of Coal $1,000 Inflation 1.60% Increase in Coal Price due to Inflation in 7 years = 1000 * 1.016^7 = $1117.552 Actual price after 7 years $1,286 Real Growth in Coal (1286 / 1117.552) 1.150761 Real Growth (1+r)^7 = 1.150761 or, 1+r = 1.150761 ^ 1/7 or, 1+r = 1.020263 or, r = 0.020263 Real Interest Rate = 0.0203 Purchase Price of Gold $1,000 Growth In Gold [(438/414) - 1] 5.7971% Increase in Gold Price due to Index in 7 years = 1000 * 1.057971 = $1057.971 Actual price after 7 years $1,288 Real Growth in Gold (1288 / 1057.971) 1.217425 Real Growth (1+r)^7 = 1.217425 or, 1+r = 1.217425 ^ 1/7 or, 1+r = 1.028504 or, r = 0.028504 Real Interest Rate = 0.0285

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