Re: a financial scenario using a 17/19BII Message #4 Posted by Werner Huysegoms on 23 June 2003, 6:01 a.m., in response to message #1 by Justin
I did this once before (albeit a bit differently), so here goes:
0. Data

. capital buildup during 20 years, with an annual payment adapted to inflation (PMT, negative).
. capital depletion over 10 years, again with an annual payment (now received) that is adapted to inflation (pmt, positive)
. basically, we'll pay PMT*E^i for i=1..20, then we'll receive pmt*E^j for j=1..10
. E = 1.035 (inflation), B = 1.08 (intrest rate)
. we assume payments to be made at the end of each period
1. Depleting the builtup sum

The first sum to be received will be pmt*E, the second pmt*E^2 and so on.
Call pv the builtup sum, then at the age of retirement the following equation holds:
0 = pv + pmt*E/B + pmt*E^2/B^2 + ... + pmt*E^n/B^n
or
0 = pv + pmt/C + pmt/C^2 + ... pmt/C^n
This is the normal TVM equation with 1+i/100 = C = B/E
now we know pmt = $50,000 in today's money. Adjusted for inflation,
that becomes:
50,000 * 1.035^20 = $ 99,489.44
with n = 10
pmt = 99,489.44
p/yr = 1
i%yr = [(1.08)/(1.035)1)]*100 = 4,347826
fv = 0
payments at END of period
this gives a pv of $ 793,155.34, and the first pmt will be $ 99,489.44 * 1.035,
because it will be made a year after retirement.
2. Building up the sum

0 = FV + PMT*E*B^(N1) + PMT*E^2*B^(N2) + ... + PMT*E^(N1)*B + PMT*E^N
after division by B^N, where C = B/E:
0 = FV/B^N + PMT/C + PMT/C^2 + ... PMT/C^N
or 0 = (FV/C^N)/E^N + ..
of course, FV = pv
again, solve with:
n = 20
p/yr = 1
i%yr = 4,347826 (no change!)
pv = 0 (don't forget!)
fv = 793,155.34 / (1.035)^20 = $ 398,612.82
PMT = 12,910.09 $, first PMT will be * 1.035
an overview of the cash flows and capital buildup and depletion:
(CAP[i] := CAP[i1]*1.08  PMT[i])
YEAR PMT CAP
1 13361,94 13361,94
2 13829,61 28260,50
3 14313,64 44834,99
4 14814,62 63236,41
5 15333,13 83628,45
6 15869,79 106188,52
7 16425,24 131108,84
8 17000,12 158597,67
9 17595,12 188880,61
10 18210,95 222202,01
11 18848,34 258826,50
12 19508,03 299040,65
13 20190,81 343154,71
14 20897,49 391504,58
15 21628,90 444453,84
16 22385,91 502396,06
17 23169,42 565757,16
18 23980,35 634998,08
19 24819,66 710617,59
20 25688,35 793155,34
21 102971,57 753636,20
22 106575,58 707351,51
23 110305,72 653633,91
24 114166,42 591758,20
25 118162,25 520936,60
26 122297,93 440313,60
27 126578,36 348960,34
28 131008,60 245868,57
29 135593,90 129944,15
30 140339,69 0,00
