Study Notes on Effective Interest Rates and Bonds

Effective Interest Rate and Compounding

• Introduction to Effective Rate

  • Example: Personal application of effective rate situation
  • Discussion about omitted slides related to amortization and rates.

• Definitions

  • APR (Annual Percentage Rate):

  • Considered a nominal rate.

  • Does not account for compounding.

  • Nominal Rate:

  • Quoted or stated interest rate, does not reflect actual earning potential.

  • E.g., earning 10% and inflation at 3% results in an effective rate of approximately 7%.

  • Effective Rate:

  • Actual rate of interest earned or paid after considering compounding.

  • Influenced by how often interest is compounded (e.g., quarterly, monthly).

  • Periodic Rate:

  • Interest charged for each compounding period.

  • Calculated by dividing the nominal rate by the number of compounding periods.

  • Example:

    • Quarterly compounding: Number of periods = 4.
    • Monthly compounding: Number of periods = 12.

• Calculating Effective Rate

  • Formula:
  • $ext{Effective Rate} = \bigg(1 + \frac{nominal ext{ rate}}{n}\bigg)^{n} - 1$
  • Where ( n ) is the number of compounding periods.
  • Example Calculation:
  • 8% nominal rate compounded quarterly:
    • Periodic rate = 8% / 4 = 2% = 0.02
    • Effective rate calculation:
    • $ext{Effective Rate} = \bigg(1 + 0.02\bigg)^{4} - 1$
    • Calculating: $1.02^{4} - 1 = 0.0824 ext{ or } 8.24$
  • Calculator method:
    • Use specific button functions for conversions (e.g., nominal and effective rates).

• Application of Effective Rate in Different Scenarios

  • Real-world implications on personal finance (credit card rates and loans).

Bond Basics

• Introduction to Bonds

  • Bonds as a form of debt issued by companies or governments to raise money.
  • Comparison with stocks - bonds provide investment opportunities and regular payments.

• Accounting Perspective

  • Bonds recorded in the liability section of the balance sheet alongside other liabilities.
  • Example of a company (Manchester University) using bonds for financing projects.

• Types of Bonds

  • Treasury Bonds:
  • Issued by the U.S. Federal Government.
  • Reflect federal debt (approx. $38 trillion).
  • Municipal Bonds:
  • Issued by state or local governments.
  • Corporate Bonds:
  • Issued by companies for capital raising.

• Bondholder vs. Shareholder

  • Bondholders have priority over shareholders during liquidation.
  • Bondholders entitled to regular interest payments and the principal (par value) upon maturity.
  • In case of esdefault, bondholders must be repaid before shareholders receive anything.

Key Terms related to Bonds

• Indenture:

  • Agreement between bondholder and bond issuer detailing payment terms and other specifics.

• Par Value:

  • Face value of the bond, typically $1,000 unless specified otherwise.

• Coupon:

  • Stated interest rate in the bond’s agreement, does not change during the bond’s life.

• Yield to Maturity (YTM):

  • Market rate of return, fluctuates according to the market conditions.
  • May also be referred to as effective rate, required return, etc.

• Bond Price:

  • Present value of future cash flows from the bond, calculated using the interest payments and maturity value.

Present Value Calculation of Bonds

• Future Cash Flows for Bonds:

  • Interest payments received throughout the life of the bond.
  • Maturity value redeemed at the end of the bond’s term.

• Steps for Calculation:

  • Present Value of Interest Payments and Present Value of Maturity Value can be calculated separately or together.
  • Example: Pricing mechanism results in amounts differing from par value, yielding premium or discount bonds.

Conclusion and Next Steps

• Importance of understanding effective rate, bonds, and present value calculations, particularly for personal finance.
• Surveys on lecture attendance and preparation for future learning in investment topics (Chapter 7).