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Chapter 4: Q.18 (page 134)

What is the yield to maturity on a simple loan for \(1,500 that requires a repayment of \)15,000 in five years?

Short Answer

Expert verified

Th Yield to Maturity on a simple loan is 58.5%

Step by step solution

01

Step 1. Introduction

Bonds are debt instruments that are issued by governments or businesses to raise funds. Bu purchasign a bond, an invest lends money to the issuer. In return, the investor gets the principal amount along with the interest at the maturity of the bond.

02

Step 2. Explanation

YieldtoMaturitywillbecalculatedas:1500=15000(1+r)^n1500=15000(1+r)^5YTM=5$15000$1500=510-1=1.5848-1=0.585=58.5%

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Most popular questions from this chapter

Go to the St. Louis Federal Reserve FRED database, and find data on the interest rate on a four-year auto loan (TERMCBAUTO48NS). Assume that you borrow \(20,000 to purchase a new automobile and that you finance it with a four-year loan at the most recent interest rate given in the database. If you make one payment per year for four years, what will the yearly payment be? What is the total amount that will be paid out on the \)20,000 loan?

Property taxes in a particular district are 2% of the purchase price of a home every year. If you just purchased a \(150,000 home, what is the present value of all the future property tax payments? Assume that the house remains worth \)150,000 forever, property tax rates never change, and a 4% interest rate is used for discounting.
Consider a bond with a 6% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?

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.

Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?
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