Assignment Question I can't find an answer too:
Assume that a series of inflation rates is 1 percent, 2 percent, and 4 percent, while nominal interest rates in the same three periods are 5 percent, 5 percent, and 6 percent, respectively.
a.What are the ex post real interest rates in the same three periods?
b.If the expected inflation rate in each period is the realized inflation rate in the previous period, what are the ex ante real interest rates in periods two and three?
c.If someone makes a loan in period two based on the ex ante inflation expectation in part b, will he or she be pleasantly or unpleasantly surprised?
a) real interest rate is nonminal rate less inflation.
b) ex ante means "before the facts" or "beforehand". So expected inflation in period 2 is inflation in period 1 = 1%.
c) the expected real interest in period 2 is interest less expected inflation = 5% - 1% = 4%. So, in period 2, the loaner got a 4% return rather than the ex post real rate of 3%. In year 3, the loaner gets a rate of 6% - 2% = 4% instead of the ex post real rate of 2%, I would say a pleasant surprise for the loaner in both years, (an unpleasant suprise for the loanee.)
a. To calculate the ex post real interest rate, we subtract the inflation rate from the nominal interest rate.
For period one:
Ex post real interest rate = Nominal interest rate - Inflation rate
Ex post real interest rate = 5% - 1% = 4%
For period two:
Ex post real interest rate = Nominal interest rate - Inflation rate
Ex post real interest rate = 5% - 2% = 3%
For period three:
Ex post real interest rate = Nominal interest rate - Inflation rate
Ex post real interest rate = 6% - 4% = 2%
b. To calculate the ex ante real interest rate, we use the expected inflation rate for each period.
For period two, the expected inflation rate is the realized inflation rate from period one, which is 1%.
Ex ante real interest rate = Nominal interest rate - Expected inflation rate
Ex ante real interest rate = 5% - 1% = 4%
For period three, the expected inflation rate is the realized inflation rate from period two, which is 2%.
Ex ante real interest rate = Nominal interest rate - Expected inflation rate
Ex ante real interest rate = 6% - 2% = 4%
c. If someone made a loan in period two based on the ex ante inflation expectation calculated in part b, they would be unpleasantly surprised because the realized inflation rate in period two is 4%, higher than the expected inflation rate of 2%. This means the purchasing power of the loan amount would be eroded more than anticipated due to higher inflation.
a. To calculate the ex-post real interest rates, we subtract the corresponding inflation rate from the nominal interest rate.
In period one:
Ex-post real interest rate = Nominal interest rate - Inflation rate
= 5% - 1%
= 4%
In period two:
Ex-post real interest rate = Nominal interest rate - Inflation rate
= 5% - 2%
= 3%
In period three:
Ex-post real interest rate = Nominal interest rate - Inflation rate
= 6% - 4%
= 2%
b. If the expected inflation rate in each period is the realized inflation rate in the previous period, we can calculate the ex-ante real interest rates as follows:
In period two:
Ex-ante real interest rate = Nominal interest rate - Expected inflation rate (which is the realized inflation rate in the previous period)
= 5% - 1%
= 4%
In period three:
Ex-ante real interest rate = Nominal interest rate - Expected inflation rate (which is the realized inflation rate in the previous period)
= 5% - 2%
= 3%
c. To determine if the borrower will be pleasantly or unpleasantly surprised, we compare the realized inflation rate in period two to the expected inflation rate used when making the loan.
Expected inflation rate in period two = Realized inflation rate in period one = 1%
Realized inflation rate in period two = 2%
Since the realized inflation rate in period two is higher than the expected inflation rate, the borrower will be unpleasantly surprised because the purchasing power of the money they borrowed will decrease more than they anticipated.
To find the answers to the questions, we need to understand the concepts of nominal interest rates, inflation rates, and real interest rates.
1. Nominal Interest Rate: It is the interest rate stated on a loan or investment, without considering inflation. It represents the actual dollar amount you will receive or pay.
2. Inflation Rate: It is the rate at which prices increase over time, causing the purchasing power of money to decrease. It is usually expressed as a percentage.
3. Real Interest Rate: It is the interest rate adjusted for inflation, representing the actual increase in purchasing power of an investment or loan. It is calculated by subtracting the inflation rate from the nominal interest rate.
Now, let's answer the questions one by one:
a. Ex post real interest rates in the three periods:
To calculate the ex post real interest rate, subtract the inflation rate from the nominal interest rate.
Period 1: Ex post real interest rate = Nominal Interest Rate - Inflation Rate = 5% - 1% = 4%
Period 2: Ex post real interest rate = Nominal Interest Rate - Inflation Rate = 5% - 2% = 3%
Period 3: Ex post real interest rate = Nominal Interest Rate - Inflation Rate = 6% - 4% = 2%
b. Ex ante real interest rates in periods two and three:
For the ex ante real interest rate, we use the expected inflation rate in each period. According to the information provided, the expected inflation rate in each period is the realized inflation rate in the previous period.
Period 2: Ex ante real interest rate = Nominal Interest Rate - Expected Inflation Rate (from Period 1) = 5% - 1% = 4%
Period 3: Ex ante real interest rate = Nominal Interest Rate - Expected Inflation Rate (from Period 2) = 6% - 2% = 4%
c. Whether someone will be pleasantly or unpleasantly surprised when making a loan depends on the actual inflation rate compared to their expectation. Since the loan in question is made in period two based on the ex ante inflation expectation, the person's expectation is a 2% inflation rate.
If the actual inflation rate in period two turns out to be less than 2%, the person will be pleasantly surprised because the purchasing power of their investment will increase more than expected. On the other hand, if the actual inflation rate exceeds 2%, the person will be unpleasantly surprised because the purchasing power of their investment will decrease more than expected.