134b.Lecture2TVM.F11

# 134b.Lecture2TVM.F11 - Annuities a fixed number of level...

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9/25/11 1 Let C be the cashflow received at time t = 1,2,. ..,n The present value of this payment stream can be written as: PV(A n ) = C (1 + r ) + C + r ) 2 + ... + C + r ) n = C n + r ) n n = 1 N Annuities : a fixed number of level, regular cash flows . Useful shortcuts : Using the standard technique to sum a finite geometric series, the present value of an annuity is PV(A n ) = C r 1 1 1 + r Λ Ν Μ Ξ Π Ο n Λ Ν Μ Μ Ξ Π Ο Ο The Future (compounded) value of the annuity at time t = n is: FV(A n )= PV(A n )(1 + r) n FV(A n )= C r (1 + r ) n 1 ( ) Perpetuities: a level series of cash flows that last forever PRESENT VALUE OF A PERPETUITY This is a special case when n PV(A )= C + r ) + C + r ) 2 + ... + C + r ) n + ... ) = C r PV(GA )= C + r ) + C + g ) + r ) 2 + ... + C + g ) n 1 + r ) n + ... Simplifying, PV(GA )= C r g Assumption: g < r otherwise the sum Can you write an expression for an annuity when cash flows grow? i.e., what is PV(GA n )? Valuing a perpetuity when cash flows grow at a constant rate

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9/25/11 2 TVM: Applications Total Interest Payments Principal Returned Amt. of Loan Year Payment
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134b.Lecture2TVM.F11 - Annuities a fixed number of level...

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