Summary: Investment Science | 9780199740086 | David G Luenberger

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• 2 The basic theory of interest

• 2.1 principal and interest

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• effective interest rate

  r' --> 1+r'=(1+(r/m))^k 

  the equivalent yearly interest rate that would produce the same result after 1 year without compounding

• effective rate of intersest conintuous compounding

  1+r'=e^r

• 2.3 present and future values of streams

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• future value of a stream 

  FV = x0(1+r)^n + x1(1+r)^n-1 + ... + xn

  
  

  Example:

  (-2, 1, 1, 1), 10%

  FV = -2(1.1)^3 + 1(1.1)^2 + 1.1 + 1 = 0.648

• present value of a stream

  PV = x0 + x1/(1+r) + x2/(1+r)^2 + ... + xn/(1+r)^n

  
  

  continuous compounding:

  PV =  xk / (1 + r/m )^k 
  

  
  

  Example:

  (-2, 1, 1, 1), 10%

  PV = -2 + 1/1.1 + 1/(1.1)^2 +1/(1.1)^3 = 0.487

• main theorem on present value

  the cash flow streams x and y are equivalent for a constant ideal bank with interest rate r iff the present values of the stream, evaluated at the bank's interest rate, are equal

  
  

  x = (x0, x1, ..., xn)

  y = (y0, y1, ..., yn)

• 2.4 Internal rate of return

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• main theorem of internal rate of return

  Suppose the cash flow stream x has x0<0 and xk0 for all k with at least one term being striclty positive. Then there is a unique positive root to the equation: 0=x0 + x1c +x2c^2 + ... + xnc^n

  
  

  Furthermore, if  xk > 0, then the corresponding internal rate of return r=(1/c)-1 is positive
  

• 3 fixed-income security

• 3.1 the market for future cash

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• time deposit account

  the interest is guaranteed, where the deposit must be maintained for a given lenght of time

• a banker's acceptance

  sell banker's acceptance to someone else at a discount before the time has expired

• variations onthe standard mortage

  -balloon payment: modestsized periodic payments for several years followed by a final balloon payment

  -adjustable-rate mortgages: mortgage adjust the effective interest rate periodically according to an interest rate index 

  
  

• 3.2 value formulas

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• perpetual annuity (perpetuity)

  fixed income instrument which pays a fixed sum periodically forever

  
  

  P= A/(1+r)^k = A/(1+r) + P/(1+r) = A/r