Question

with no inflation, a bank would be willing to lend a business firm $5 million at an annual interest rate of 6 percent. but if the rate of inflation was anticipated to be 4 percent, the bank would most likely charge the firm an annual interest rate of

Answer 1

In anticipation of a 4 percent inflation rate, the bank would likely charge the firm an annual interest rate of approximately 10.4 percent to maintain the real return on the loan.

Step-by-step explanation:

In the absence of inflation, the bank is willing to lend $5 million at a 6 percent annual interest rate. However, when inflation is expected at 4 percent, the real return the bank receives diminishes. To maintain the same real interest rate, the nominal interest rate must increase. The Fisher equation, which relates nominal interest rates, real interest rates, and inflation, can be expressed as follows:

`\[1 + \text{Nominal Interest Rate} = (1 + \text{Real Interest Rate}) * (1 + \text{Inflation Rate})\]`

Substituting the given values:

`\[1 + \text{Nominal Interest Rate} = (1 + 0.06) * (1 + 0.04)\]`

Solving for the nominal interest rate:

`\[\text{Nominal Interest Rate} = 1.06 * 1.04 - 1 \approx 1.104 - 1 = 0.104\]`

Convert to a percentage:

`\[\text{Nominal Interest Rate} \approx 0.104 * 100 \approx 10.4\%\]`

Therefore, in anticipation of a 4 percent inflation rate, the bank would likely charge the firm an annual interest rate of approximately 10.4 percent to maintain the real return on the loan. This adjustment compensates for the reduction in the real value of money due to inflation.