Dennis buys a house in 1973 and finances it with a mortgage that carries an annual interest rate of 7 per cent. Inflation in 1973 is 3 per cent, inflation in 1974 is 4 per cent, and inflation in 1975 is 5 per cent. The real interest rate Dennis would pay on his mortgage in 1974 is __%.

Question

BlackTom AI · Accepted Answer

The Fisher relation links nominal and real interest rates: (1 + nominal rate) = (1 + real rate) × (1 + inflation). Thus real rate = (1 + nominal)/(1 + inflation) − 1.

Given: nominal mortgage rate = 7% = 0.07, inflation in 1974 = 4% = 0.04. Apply the formula step by step:
1 + nominal = 1 + 0.07 = 1.07
1 + inflation = 1 + 0.04 = 1.04
Divide: 1.07 / 1.04 = 1.0288461538
Subtract 1: 1.0288461538 − 1 = 0.0288461538

Convert to percent: 0.0288461538 × 100% = 2.88461538%, approximately 2.885%.

A common approximation (valid when rates are small) is real ≈ nominal − inflation = 7% − 4% = 3%. The exact Fisher calculation gives about 2.885%, which rounds to 3% to the nearest whole percent. That is why the provided answer is 3%.

Why other approaches would be wrong: using 1973 or 1975 inflation instead of 1974 would misstate the real cost for 1974. Using cumulative inflation across years is irrelevant for the single-year real interest rate. The nominal minus inflation approximation is close but slightly above the exact value (difference ≈ 0.115 percentage points) because the exact formula accounts for compounding.

Conclusion: the real interest Dennis pays in 1974 is approximately 2.885%, which rounds to 3%, matching the provided answer of 3%.

Dennis buys a house in 1973 and finances it with a mortgage that carries an annual interest rate of 7 per cent. Inflation in 1973 is 3 per cent, inflation in 1974 is 4 per cent, and inflation in 1975 is 5 per cent. The real interest rate Dennis would pay on his mortgage in 1974 is __%. 数值题

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