Compute the real interest rate using the exact formula and...

Compute the real interest rate using the exact formula and the approximation formula for each set of assumptions listed in (a) to (c).
a. $i=4 \%_i p^e=2 \%$
b. $i=15 \% ; p^2=11 \%$
c. $i=54 \%_j p^6=46 \%$
d. $i=0 \%_i p^\epsilon=5 \%$

Key Concepts

Nominal Interest Rate

This is the stated rate of interest before adjusting for inflation. It represents the percentage increase in money that lenders receive for providing funds, without accounting for changes in the purchasing power of money over time.

Inflation Rate

The inflation rate signifies the rate at which prices for goods and services are rising, thereby eroding the purchasing power of money. In many contexts, especially when considering real returns, it is important to differentiate between the nominal rate and the inflation rate.

Exact Real Interest Rate Calculation (Fisher Equation)

The exact formula for the real interest rate is based on the Fisher Equation, which is mathematically expressed as r = (1 + i) / (1 + ?) - 1, where i is the nominal interest rate and ? is the inflation rate. This formula accurately accounts for the compounding effects of inflation on the nominal interest rate, providing a precise measure of the real return.

Approximate Real Interest Rate Calculation

The approximate formula for computing the real interest rate is r ? i - ?. This approximation is often used for simplicity, particularly when both the nominal interest rate and the inflation rate are relatively small, such that the compounding effects are minimal. However, as the rates increase, the approximation may deviate from the exact calculation.

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