You are trying to estimate the real interest rate for the mining industry produc
ID: 2765483 • Letter: Y
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
When you borrow or lend, you normally do so in dollar terms. If you take out a loan, the loan is denominated in dollars, and your promised payments are denominated in dollars. These dollar flows must be corrected for inflation to calculate the repayment in real terms. A similar point holds if you are a lender: you need to calculate the interest you earn on saving by correcting for inflation.
The Fisher equation provides the link between nominal and real interest rates. To convert from nominal interest rates to real interest rates, we use the following formula:
REAL INTEREST RATE NOMINAL INTEREST RATE INFLATION RATE
Nomial Interest rate (Coal) :
$1281 = $1000 (1+i)8
Interest rate
0.0315
opening
interet
Total
1
1000
31.5
1031.5
2
1031.5
32.49225
1063.992
3
1063.99225
33.51576
1097.508
4
1097.508006
34.5715
1132.08
5
1132.079508
35.6605
1167.74
6
1167.740013
36.78381
1204.524
7
1204.523823
37.9425
1242.466
8
1242.466323
39.13769
1281.604
I = 0.0315 or 3.15%
Inflation = 1.6% per year
Real Interest rate = 3.15% - 1.6%
Real Interest rate = 1.55%
Nomial Interest rate (Gold) :
$1279 = $1000 (1+i)8
Interets rate
0.03124
opening
interet
Total
1
1000
31.24
1031.24
2
1031.24
32.21594
1063.456
3
1063.455938
33.22236
1096.678
4
1096.678301
34.26023
1130.939
5
1130.938531
35.33052
1166.269
6
1166.269051
36.43425
1202.703
7
1202.703296
37.57245
1240.276
8
1240.275747
38.74621
1279.022
I = 0.0312 or 3.12%
Inflation = 0.00225 or 0.225%
Interets rate
0.00225
opening
interet
Total
1
417
0.93825
417.9383
2
417.93825
0.940361
418.8786
3
418.8786111
0.942477
419.8211
4
419.8210879
0.944597
420.7657
5
420.7656854
0.946723
421.7124
6
421.7124082
0.948853
422.6613
7
422.6612611
0.950988
423.6122
8
423.6122489
0.953128
424.5654
Real interest rate = 3.12% - 0.0225%
Real Interest rate = 3.0975
Interest rate
0.0315
opening
interet
Total
1
1000
31.5
1031.5
2
1031.5
32.49225
1063.992
3
1063.99225
33.51576
1097.508
4
1097.508006
34.5715
1132.08
5
1132.079508
35.6605
1167.74
6
1167.740013
36.78381
1204.524
7
1204.523823
37.9425
1242.466
8
1242.466323
39.13769
1281.604
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