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 8 years from now, the selling values in actual dollars are predicted to be $1281 (coal) and $1279 (gold).

Inflation (for coal) is 1.6% per year, for the next 8 years. For gold, the gold price index is predicted to rise in the next 8 years from the current 417 points to 424 points.

Compute the estimated real interest rate, as a number, with 0.001 precision.

Explanation / Answer

The real interest rate for coal is calculated as follows:

The nominal rate for coal is =1000(1+r)^8 = 1281

(1+r)^8 = 1281/1000 = 1.281

1+r =(1.281)^(1/8)

r = 0.03144

Real rate = (nr-ir)/(1+ir) where nr = nominal rate = 0.03144 and ir = inflation rate = 0.016

Real rate for coal = (0.03144-0.016)/1.016 = 0.015

The real interest rate for gold ias as follows

The nominal rate for gold is =1000(1+r)^8 = 1279

(1+r)^8 = 1281/1000 = 1.279

1+r =(1.279)^(1/8)

r = 0.03124

The nominal rate = nr = 0.03124

The inflation rate ir is calculated as follows

(1+ir) =( 424/417)^(1/8)

So inflation rate = 0.00208

So the real rate for gold=( 0.03124-0.00208)/1.00208 = 0.029

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