Question

3. Suppose you take out a loan for school this year for $4500. The bank expects that the rate of inflation for next year will equal 2%. You and the bank agree that in one year's time, you will pay back the full amount at an interest rate of 6%. Next year though, there is a sudden rise in inflation, causing inflation to equals 7%. a. How much will you pay back in one year? b. What is the anticipated rate of inflation? c. What is the unanticipated rate of inflation? d. What is the real rate of interest? What is the nominal rate of interest? f. Who wins and who loses from this loan? е.

Answer 1

3. a) Given information are

Loan = 4500

Interest rate = 6%

Loan period = 1 year

At the end of year 1, we pay back the loan amount along with interest on loan. Interest charged on loan can be calculated as

interest paid = 4500*6/100

= 270

Amount paid back at the maturity of the loan is

= loan amount + interest paid

= 4500+270

= 4770

b) Anticipated inflation rate is the increase in general price level expected by the market participants in the economy for a given time period.

In the above question anticipated inflation rate is 2%. I.e the banks expects the inflation rate at the end of year one to be 2%.

The 7% inflation rate at the end of year one is the actual inflation level in the economy.

c) Unanticipated inflation - inflation rate that is not expected by the market participants in the economy. In the above question, people expected the inflation to be 2% at the end of year one. But the actual inflation turned out be 7%. I.e inflation over shot by 5% than expected. 7% is the unanticipated rate of inflation.

d) Real interest rate - it shows real cost of borrowing or the real yield the lender receives after removing inflationary effects. The formula for real interest rate calculation can be written as

Nominal interest rate = Real interest rate + inflation rate

Real interest rate = Nominal interest rate - inflation rate

In the above question, nominal interest rate is 6%, inflation rate is 2% therefore real interest rate is

real interest rate = 6% - 2%

= 4%

e) Nominal interest rate - interest rate charged on loan amount. It is the interest rate before taking inflation into consideration.

Nominal interest rate = real interest rate + inflation rate

= 4% + 2%

= 6%

f) To understand who wins or lose, we need to calculate interest paid by us taking into the two inflationary situations give.

At 2% inflation rate, nominal interest rate is 6%. Therefore interest paid by us is 270 ( 4500*6/100 )

At the end of year one actual inflation turned out to be 7%. Nominal interest rate in this situation will be

Nominal interest rate = real interest rate + inflation rate

= 4% + 7%

= 11%

Interest paid by us at 11% nominal rate is

interest paid = 4500 * 11/100

= 495

The interest paid for the loan amount is fixed at 6% given the anticipated inflation of 2%. So we are actually paying only 270 as interest.

But since the actual inflation turned out be 7%, what we had end up paying would be 495. i.e we would have to pay 225 extra.

Nominal interest rate is calculated on anticipated inflation rate.

Therefore, we as a borrower, make a saving of 225 given the actual inflation rate of 7%.

Lender is the loser and the borrower is the winner in this scenario. What we are giving to the lender is less than what it should be given the inflation of 7%.