Question

6. Suppose you walk into a bank to borrow money for a new car. The loan officer tells you that they will loan you $10,000 for the car at a simple interest rate of 5.3 percent per year. You must repay the loan at the end of the year.

a) How much interest will you have to pay?

b) The bank expects that the inflation rate will be 2.2 percent over the year. What does the bank think that the real interest rate will be?

c) You expect that the inflation will be 3 percent. What do you think the real interest rate will be?

d) Does the bank or you as a borrower benefit the most if the inflation rate is only 1 percent?

Answer 1

Ans. Loan Amount, L = $10000

Interest rate charged, r = 5.3% or 0.053

a) Total interest in 1 year paid = r*L = 0.053*10000 = $530

b) From Fisher Equation,

Nominal Interest Rate = Real Interest Rate + Inflation

=> 5.3 = Real Interest Rate + 2.2

=> Real Interest Rate = 5.3 - 2.2 = 3.1%

Thus, bank expects a real interest rate of 3.1%

c) From Fisher Equation,

Real interest rate = 5.3 - 3 = 2.3%

Thus, I expect a real interest rate of 2.3%

d) If inflation rate turns out to 1%,

Then, real interest rate = 5.3 - 1 = 4.3%

Thus, I have to pay a higher real interest rate of 4.3% and bank earns a higher than expected real interest rate of 4.3%. Thus, bank benefits from the lower than expected inflation rate.

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