Question

3. Suppose you take out a loan for school this year for $9000. 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 5%. Next year though, there is a sudden

      rise in inflation, causing inflation to equal 12%.

      Based upon this information, answer the following questions.

1. 1. How much will you pay back in one year, assuming simple interest?
2. What is the anticipated rate of inflation?
3. What is the unanticipated rate of inflation?
4. What is the real rate of interest?
5. What is the nominal rate of interest?
6. Who wins and who loses from this loan?

Answer 1

(a)

Amount borrowed = $9,000

The amount is to be repaid in one year's time.

Time period = 1 year

Interest rate = 5% or 0.05

Calculate the amount of interest to be paid -

Amount of interest to be paid = Amount borrowed * Interest rate * Time period = $9,000 * 0.05 * 1 = $450

The amount of interest to be paid is $450.

Calculate the amount to be paid back in one year -

Amount to be paid back in one year = Amount borrowed + Amount of interest to be paid = $9,000 + $450 = $9,450

Thus,

The amount to be paid back in one year is $9,450

(b)

Anticipated rate of inflation is the expected rate of inflation.

The expected rate of inflation is 2%.

Thus,

The anticipated rate of inflation is 2%.

(c)

Unanticipated rate of inflation is the actual rate of inflation.

The actual rate of inflation is 12%.

Thus,

The unanticipated rate of inflation is 12%.

(d)

Calculate the real rate of interest -

Real rate of interest = Interest rate charged on loan - Actual inflation rate

Real rate of interest = 5% - 12% = -7%

Thus,

The real rate of interest is -7%.

(e)

The rate of interest charged by the bank on amount borrowed is the nominal rate of interest.

The rate of interest charged by the bank on amount borrowed is 5%.

Thus,

The nominal rate of interest is 5%.

(f)

When unanticipated inflations turns out to be greater than the anticipated inflation then borrower wins and lender loses.

In the given case, unanticipated inflation is greater than the anticipated inflation.

Thus,

The borrower (the person taking the loan) wins and the bank loses from this loan.