© 2000 John Petroff
|
|
© 2000 John Petroff |
Appendix to Chapter 2
Derivation of the present value annuity factor for an annuity in perpetuity.
If i = interest rate and n= number of years to maturity, the
sum S of individual present value factors is
S = 1/(1+i) + 1/(1+i)2 + ... + 1/(1+i)n-1 + 1/(1+i)n
This sum can be multiplied by (1 + i),
(1 + i)S = 1+ 1/(1+i) + 1/(1+i)2 + ... + 1/(1+i)n-1
Subtracting the first equation from the second reduces to
(1+i)S - S = 1 - 1/(1+i)n
S = (1 - 1/(1+i)n )/i
As n tends to infinity, 1/(1+i)n tends to zero and S becomes
S = 1/i
| Previous: Assignments |
|
Next: Comments |