Question

1. What is the relationship between real interest rate, nominal interest rate and inflation rate?

2. What are the reasons for very high nominal interest rates in the 1980s?

3. Someone buys a 5 year government treasury bond at $P

t

a.

Can the price be above face value? Why?

b. Can the price be below face value? Why?

c.

If he/she wants to sell it after 2 years, will he/she makes a positive rate of return or

negative rate of return? Explain.

4. Consider the following bond purchased at $800 in 2018.

F=1000; C=100; N=5; P=800

a.

What is the yield to maturity? (This is equal to the market interest rate prevailing in

2018)

b. If the interest rate rises to 20% in 2019 what is the price of the bond?

(Solve the following equation: 0.2=(100+(1000-P)/5)/(1000+P)/2

c.

If the investor sold the bond in 2019 without holding till maturity did he/she make a

profit or a loss?

d. What is the rate of return in 2019?

Answer 1

Answer 1:

The simplest type of interest rate is the nominal interest rate.It is the stated interest rate of a given bond or loan. It is the price which the borrowers have to pay the lenders to use their money. If the borrower takes a loan of $100 with 5 per cent nominal rate of interest, then the borrower will have to pay lender $5 on the $100 loan taken from the lender. Thus, nominal rate of interest does not take into account the inflation rate in the economy.

However, the rate of interest which takes inflation into account is real rate of interest. Taking the example, above, if the rate of inflation in the economy is currently 5 per cent means that the average basket of goods purchased this year is 5 per cent more expensive than the basket of goods purchased last year, thus in the previous example, the lender will make nothing if he loaned the money at 5 per cent when the inflation rate is 5 per cent. Thus, real rate of interest or real rate of return on the money is 0 per cent.

Thus, the formula depicting the relationship between nominal rate of interest, inflation rate and real rate of interest is :

Real Interest Rate = Nominal Interest Rate - Inflation Rate

This means when rate of inflation is zero, then real interest rate is equal to nominal rate of interest. With positive inflation rate, nominal interest rate is higher than real interest rate and negative inflation rate, real rate of interest will exceed the nominal rate of interest in the economy.