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Chapter 4: Q.25 (page 134)

Assume you just deposited \(1,250 into a bank account. The current real interest rate is 1%, and the expected rate of inflation over the next year is 5%. What nominal interest rate should the bank charge you over the next year? How much money will you have at the end of one year? If you are saving to buy a motorbike that currently sells for \)1,300, will you have enough money to buy it?

Short Answer

Expert verified

The money will not be enough to buy motorcycle

Step by step solution

01

Step 1. Introduction

Interest rates are the amount charged on loans by lenders. It also refers to the amount paid to depositors on deposit. Nominal interest rate refers tot he interest rate that is not adjusted for inflation.

02

Step 2. Explanation

Real Interest Rate=1%

Inflation Rate=5%

NominalInterestRate=RealInterestRate+InflationRate=1%+5%=6%or0.06Amountafteroneyear=Deposit脳(1+NominalInterestRate)=$1250脳(1+0.06)=$1325Costofmotorcycleinoneyear=Currentcostofmototrcycle脳(1+inflationrate)=$1300脳(1+0.05)=$1,365

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Most popular questions from this chapter

What is the formula used to calculate the yield to maturity on a 20-year coupon bond with a current yield of 12% and \(1,000 face value that sells for \)2,500

If the interest rate is 15%, what is the present value of a security that pays you \(1,100 next year, \)1,250 the year after, and $1,347 the year after that?

Interest rates were lower in the mid-1980s than in the late 1970s, yet many economists have commented that real interest rates were actually much higher in the mid1980s than in the late 1970s. Does this make sense? Do you think that these economists are right?

Calculate the present value of a $1,300 discount bond with seven years to maturity if the yield to maturity is 8%.

The U.S. Treasury issues some bonds as Treasury Inflation Indexed Securities, or TIIS, which are bonds adjusted for inflation; hence the yields can be roughly interpreted as real interest rates. Go to the St. Louis Federal Reserve FRED database, and find data on the following TIIS bonds and their nominal counterparts. Then answer the questions below.

  • 5-year U.S. Treasury (DGS5) and 5-year TIIS (DFII5)
  • 7-year U.S. Treasury (DGS7) and 7-year TIIS (DFII7)
  • 10-year U.S. Treasury (DGS10) and 10-year TIIS (DFII10)
  • 20-year U.S. Treasury (DGS20) and 20-year TIIS (DFII20)
  • 30-year U.S. Treasury (DGS30) and 30-year TIIS (DFII30)

a. Following the Great Recession of 2008鈥� 2009, the 5-, 7-, 10-, and even the 20-year TIIS yields became negative for a period of time. How is this possible?

b. Using the most recent data available, calculate the difference between the yields for each of the pairs of bonds (DGS5 鈥� DFII5, etc.) listed above. What does this difference represent?

c. Based on your answer to part (b), are there significant variations among the differences in the bond-pair yields? Interpret the magnitude of the variation in differences among the pairs.
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