Topic 2 - Meaning of Interest Rates

• Interest rates


  • Link the present to the future
  • Tell the future reward for lending today
  • Tell the cost of borrowing now and repaying later
• Credit is one of the critical mechanisms we have for allocating resources
• Future Value (FV)


  The value on some future date of an investment made today
• Calculating Future Value

  FV = PV + PV × (i) = PV × (1 + i)
• The higher the interest rate or the higher the amount invested, the higher the future value
• Calculating Future Value with compound interest

  FV = PV × (1 + i)n
• In computing future value, both the interest rate and n must be measured in the same time units

  
• If the annual interest rate is 5%, the monthly rate is 0.41%
• Basis point

  One one-hundredth of a percentage point, 0.01%
• Present Value (PV)


  The value today (in the present) of a payment that is promised to be made in the future
• Calculating Present Value

  PV = FV / (1+i)n
• The present value is higher, the higher the future value of the payment, the shorter the time period until payment, and the lower the interest rate

  
• Doubling the future value of the payment, without changing the time of the payment or the interest rate, doubles the present value
• The sooner a payment is to be made, the more it is worth
• Bond


  A promise to make a series of payments on specific future dates
• Types of bonds

  • Zero-coupon or discount bonds
  • Fixed-payment loans
  • Coupon bonds
  • Consol or Perpetuity
• Zero-coupon bonds

  Represent a promise to pay a certain amount on a fixed future date, with no coupon payments
• Calculating price of a zero-coupon bond

  1. Price of a one-year zero-coupon bond: Face Value / (1 + i)

  2. Price of a six-month zero-coupon bond: Face Value / (1 + i)1/2
• Fixed-payment loans

  Conventional home mortgages and car loans
• Calculating value of a fixed-payment loan

  Fixed Payment / (1 + i) + Fixed Payment / (1 + i)2 + ... + Fixed Payment / (1 + i)n
• Coupon bonds

  The issuer promises to make a series of periodic interest payments (coupon payments), plus a principal payment at maturity
• Calculating price of a coupon bond

  Coupon Payment / (1 + i) + Coupon Payment / (1 + i)2 +...+ Coupon Payment / (1 + i)n + Face Value / (1 + i)n
• Consol or Perpetuity

  The issuer promises to make a series of periodic interest payments forever
• Calculating price of a consol

  Yearly Coupon Payment / i
• Bond yield

  A measure of the cost of borrowing and the reward for lending
• Types of bond yields

  • Nominal yield
  • Yield to maturity
  • Current yield
• A fundamental property of a bond is that its price changes in the opposite direction to the change in the required yield
• Bond types based on price


  • Par Bond
  • Discount Bond
  • Premium Bond
• Holding Period Return

  The return of holding a bond and selling it before maturity
• The longer the term of the bond, the greater the price movements and associated risks can be
• Nominal Interest Rates (i)


  The interest rate expressed in current-pound terms
• Real Interest Rates (r)


  The inflation adjusted interest rate
• Calculating Real Interest Rate

  r = i - πe
• The higher expected inflation, the higher the nominal interest rate
• Financial markets quote nominal interest rates, and when people use the term interest rate, they are referring to the nominal rate