engm 661 engineering economics for managers investmentworth investment worth
DESCRIPTION
MARR MARR is company specific u utilities - MARR = % u mutuals - MARR = % u new venture - MARR = % MARR based on u firms cost of capital u Price Index u Treasury billsTRANSCRIPT
ENGM 661 Engineering Economics for Managers
Investment Worth
Investment Worth
MARR
Suppose a company can earn 12% / annum in U. S. Treasury bills
No way would they ever invest in a project earning < 12%
Def:The Investment Worth of all projects are measured at the Minimum Attractive
Rate of Return (MARR) of a company.
MARR
MARR is company specific
utilities - MARR = 10 - 15%
mutuals - MARR = 12 - 18%
new venture - MARR = 20 - 30%
MARR based on
firms cost of capital
Price Index
Treasury bills
Investment Worth Alternatives
NPW(MARR) > 0Good Investment
Investment Worth Alternatives
NPW(MARR) > 0Good Investment
EUAW(MARR) > 0Good Investment
Investment Worth Alternatives
NPW(MARR) > 0Good Investment
EUAW(MARR) > 0Good Investment
IRR > MARRGood Investment
Present Worth
Example: Suppose you buy and sell a piece of equipment.
Purchase Price $16,000Sell Price (5 years) $ 4,000Annual Maintenance $ 3,000Net Profit Contribution $ 6,000MARR 12%
Is it worth it to the company to buy the machine?
Present Worth
NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5)
16,000
6,000
3,000
5
0
4,000
16,000
3,000
5
0
4,000
Present Worth
NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5)
= -16 +3(3.6048) + 4(.5674)
16,000
6,000
3,000
5
0
4,000
16,000
3,000
5
0
4,000
Present Worth
NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5)
= -16 +3(3.6048) + 4(.5674)
= -2.916
= -$2,916
16,000
6,000
3,000
5
0
4,000
16,000
3,000
5
0
4,000
Annual Worth
Annual Worth (AW or EUAW)
AW(i) = PW(i) (A/P, i%, n)
= [ At (P/F, i%, t)](A/P, i%, n)
AW(i) = Annual Worth of Investment
AW(i) > 0 **OK Investment**
Annual Worth; Example
Repeating our PW example,
we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)
3,000
5
0
4,000
16,000
Annual Worth; Example
Repeating our PW example,
we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)
= -16(.2774) + 3 + 4(.1574)
3,000
5
0
4,000
16,000
Annual Worth; Example
Repeating our PW example,
we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)
= -16(.2774) + 3 + 4(.1574)
= -.808
= -$808
3,000
5
0
4,000
16,000
Alternately
AW(12) = PW(12) (A/P, 12%, 5)
= -2.92 (.2774)
= - $810 < 0 NO GOOD
3,000
5
0
4,000
16,000
Internal Rate of Return
Internal Rate-of-Return
IRR - internal rate of return is that return for which NPW(i*) = 0
i* = IRR
i* > MARR **OK Investment**
Internal Rate of Return
Internal Rate-of-Return
IRR - internal rate of return is that return for which NPW(i*) = 0
i* = IRR
i* > MARR **OK Investment**
Alt:
FW(i*) = 0 = At(1 + i*)n - t
Internal Rate of Return
Internal Rate-of-Return
IRR - internal rate of return is that return for which NPW(i*) = 0
i* = IRR
i* > MARR **OK Investment**
Alt:
FW(i*) = 0 = At(1 + i*)n - t
PWrevenue(i*) = PWcosts(i*)
Internal Rate of Return
Example
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
3,000
5
0
4,000
16,000
Internal Rate of Return
Example
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
3,000
5
0
4,000
16,000
Internal Rate of Return
Example
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i* = 5 1/4 %
i* < MARR
3,000
5
0
4,000
16,000
Public School Funding
Sheet: Sheet1
Sheet: Sheet2
Sheet: Sheet3
Sheet: Sheet4
Sheet: Sheet5
Sheet: Sheet6
Sheet: Sheet7
Sheet: Sheet8
Sheet: Sheet9
Sheet: Sheet10
Sheet: Sheet11
Sheet: Sheet12
Sheet: Sheet13
Sheet: Sheet14
Sheet: Sheet15
Sheet: Sheet16
104.5
109.20249999999999
114.11661249999997
119.25186006249996
124.61819376531244
130.2260124847515
136.0861830465653
142.21006128366074
148.60951404142546
159.01218002432526
170.14303262602803
182.05304490985
194.79675805353952
208.4325311172873
223.02280829549744
238.6344048761823
Public School Funding
216%
16 yrs
Sheet: Sheet1
Sheet: Sheet2
Sheet: Sheet3
Sheet: Sheet4
Sheet: Sheet5
Sheet: Sheet6
Sheet: Sheet7
Sheet: Sheet8
Sheet: Sheet9
Sheet: Sheet10
Sheet: Sheet11
Sheet: Sheet12
Sheet: Sheet13
Sheet: Sheet14
Sheet: Sheet15
Sheet: Sheet16
104.5
109.20249999999999
114.11661249999997
119.25186006249996
124.61819376531244
130.2260124847515
136.0861830465653
142.21006128366074
148.60951404142546
159.01218002432526
170.14303262602803
182.05304490985
194.79675805353952
208.4325311172873
223.02280829549744
238.6344048761823
School Funding
1
2
3
16
100
216
F = P(F/P,i*,16)
(F/P,i*,16) = F/P = 2.16
(1+i*)16 = 2.16
School Funding
(1+i*)16 = 2.16
16 ln(1+i*) = ln(2.16) = .7701
1
2
3
16
100
216
School Funding
(1+i*)16 = 2.16
16 ln(1+i*) = ln(2.16) = .7701
ln(1+i*) = .0481
1
2
3
16
100
216
School Funding
(1+i*)16 = 2.16
16 ln(1+i*) = ln(2.16) = .7701
ln(1+i*) = .0481
(1+i*) = e.0481 = 1.0493
1
2
3
16
100
216
School Funding
(1+i*)16 = 2.16
16 ln(1+i*) = ln(2.16) = .7701
ln(1+i*) = .0481
(1+i*) = e.0481 = 1.0493
i* = .0493 = 4.93%
1
2
3
16
100
216
School Funding
We know i = 4.93%, is that significant growth?
1
2
3
16
100
216
School Funding
We know i = 4.93%, is that significant growth?
Suppose inflation = 3.5% over that same period.
1
2
3
16
100
216
School Funding
We know i = 4.93%, is that significant growth?
Suppose inflation = 3.5% over that same period.
d= 1.4%
1
2
3
16
100
216
d
i
j
j
1
0493
0350
1
0350
.
.
.
School Funding
We know that d, the real increase in school funding
after we discount for the effects of inflation
is 1.4%.
So schools have experienced a real increase in
funding?
1
2
3
16
100
216
School Funding
We know that d, the real increase in school funding
after we discount for the effects of inflation
is 1.4%.
So schools have experienced a real increase in
funding?
Rapid City growth rate 3% / yr.
1
2
3
16
100
216
Summary
NPW > 0 Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
IRR > MARR Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
IRR > MARR Good Investment
Note: If NPW > 0 EUAW > 0
IRR > MARR
Internal Rate of Return
Internal Rate-of-Return
IRR - internal rate of return is that return for which NPW(i*) = 0
i* = IRR
i* > MARR **OK Investment**
Alt:
FW(i*) = 0 = At(1 + i*)n - t
PWrevenue(i*) = PWcosts(i*)
Internal Rate of Return
Example
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
3,000
5
0
4,000
16,000
Internal Rate of Return
Example
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i* = 5 1/4 %
i* < MARR
3,000
5
0
4,000
16,000
Spreadsheet Example
Sheet: Unit 5
Sheet: IRR
Sheet: ERR
Sheet: Mortgage1
Sheet: Mortgage2
Sheet: Retire
Sheet: Increment
Sheet: Sheet5
Sheet: Sheet6
Sheet: Sheet7
Sheet: Sheet8
Sheet: Sheet9
Sheet: Sheet10
Sheet: Sheet11
Sheet: Sheet12
Sheet: Sheet13
Sheet: Sheet14
Sheet: Sheet15
Sheet: Sheet16
Example
Period
Cash Flow
MARR =
0.12
NPV =
-2915.96397009059
=NPV(E9,C5:C9)+C4
PMT =
-808.916783292587
=-PMT(E9,5,C10)
IRR =
0.052424697816016316
=IRR(C4:C9,E9)
Example:
External Rate Return
Period
Cash Flow
Period
Cash Flow
i =
NPV =
0.05
20.408163265306598
0.1
9.0157776108191
MARR =
0.15
0.15000000000000002
2.8766335168895694
NPV =
2521.3641349996687
=NPV(E13,C7:C13)+E6
0.2
0.0
PMT =
606.0360002832754
=-PMT(E13,7,C14)
0.25
-0.9600000000000364
IRR =
0.19613045412831231
=IRR(C6:C13,0.15)
0.3
-0.9103322712792306
0.35
-0.4572473708275311
0.39999999999999997
1.1368683772161603E-13
0.44999999999999996
0.20501045553317
0.49999999999999994
0.0
0.5499999999999999
-0.7049108791245544
0.6
-1.9531250000002274
Example: # 7.8
Example: # 7.8
i =
0.01
NPV =
48981.89480090659
IRR =
0.014587838774665705
=IRR(E29:E173,0.15)
IRR =
0.17521428245349427
=IRR(J29:J41,0.15)
Period
Cash Flow
Annual Maint
Net Cash
Period
Cash Flow
Annual Maint
Net Cash
-130000.0
-130000.0
1.0
2000.0
2000.0
1.0
21500.0
2.0
2000.0
2000.0
2.0
21500.0
3.0
2000.0
2000.0
3.0
20800.0
4.0
2000.0
2000.0
4.0
21500.0
5.0
2000.0
2000.0
5.0
21500.0
6.0
2000.0
2000.0
6.0
20800.0
7.0
2000.0
2000.0
7.0
21500.0
8.0
2000.0
2000.0
8.0
21500.0
9.0
2000.0
2000.0
9.0
20800.0
10.0
2000.0
2000.0
10.0
21500.0
11.0
2000.0
2000.0
11.0
21500.0
12.0
-500.0
12.0
204000.0
-3200.0
200800.0
13.0
2000.0
2000.0
14.0
2000.0
2000.0
15.0
2000.0
2000.0
16.0
2000.0
2000.0
17.0
2000.0
2000.0
18.0
2000.0
2000.0
19.0
2000.0
2000.0
20.0
2000.0
2000.0
21.0
2000.0
2000.0
22.0
2000.0
2000.0
23.0
2000.0
2000.0
24.0
-500.0
25.0
2000.0
2000.0
26.0
2000.0
2000.0
27.0
2000.0
2000.0
28.0
2000.0
2000.0
29.0
2000.0
2000.0
30.0
2000.0
2000.0
31.0
2000.0
2000.0
32.0
2000.0
2000.0
33.0
2000.0
2000.0
34.0
2000.0
2000.0
35.0
2000.0
2000.0
36.0
-1200.0
37.0
2000.0
2000.0
38.0
2000.0
2000.0
39.0
2000.0
2000.0
40.0
2000.0
2000.0
41.0
2000.0
2000.0
42.0
2000.0
2000.0
43.0
2000.0
2000.0
44.0
2000.0
2000.0
45.0
2000.0
2000.0
46.0
2000.0
2000.0
47.0
2000.0
2000.0
48.0
-500.0
49.0
2000.0
2000.0
50.0
2000.0
2000.0
51.0
2000.0
2000.0
52.0
2000.0
2000.0
53.0
2000.0
2000.0
54.0
2000.0
2000.0
55.0
2000.0
2000.0
56.0
2000.0
2000.0
57.0
2000.0
2000.0
58.0
2000.0
2000.0
59.0
2000.0
2000.0
60.0
-500.0
61.0
2000.0
2000.0
62.0
2000.0
2000.0
63.0
2000.0
2000.0
64.0
2000.0
2000.0
65.0
2000.0
2000.0
66.0
2000.0
2000.0
67.0
2000.0
2000.0
68.0
2000.0
2000.0
69.0
2000.0
2000.0
70.0
2000.0
2000.0
71.0
2000.0
2000.0
72.0
-1200.0
73.0
2000.0
2000.0
74.0
2000.0
2000.0
75.0
2000.0
2000.0
76.0
2000.0
2000.0
77.0
2000.0
2000.0
78.0
2000.0
2000.0
79.0
2000.0
2000.0
80.0
2000.0
2000.0
81.0
2000.0
2000.0
82.0
2000.0
2000.0
83.0
2000.0
2000.0
84.0
-500.0
85.0
2000.0
2000.0
86.0
2000.0
2000.0
87.0
2000.0
2000.0
88.0
2000.0
2000.0
89.0
2000.0
2000.0
90.0
2000.0
2000.0
91.0
2000.0
2000.0
92.0
2000.0
2000.0
93.0
2000.0
2000.0
94.0
2000.0
2000.0
95.0
2000.0
2000.0
96.0
-500.0
97.0
2000.0
2000.0
98.0
2000.0
2000.0
99.0
2000.0
2000.0
100.0
2000.0
2000.0
101.0
2000.0
2000.0
102.0
2000.0
2000.0
103.0
2000.0
2000.0
104.0
2000.0
2000.0
105.0
2000.0
2000.0
106.0
2000.0
2000.0
107.0
2000.0
2000.0
108.0
-1200.0
109.0
2000.0
2000.0
110.0
2000.0
2000.0
111.0
2000.0
2000.0
112.0
2000.0
2000.0
113.0
2000.0
2000.0
114.0
2000.0
2000.0
115.0
2000.0
2000.0
116.0
2000.0
2000.0
117.0
2000.0
2000.0
118.0
2000.0
2000.0
119.0
2000.0
2000.0
120.0
-500.0
121.0
2000.0
2000.0
122.0
2000.0
2000.0
123.0
2000.0
2000.0
124.0
2000.0
2000.0
125.0
2000.0
2000.0
126.0
2000.0
2000.0
127.0
2000.0
2000.0
128.0
2000.0
2000.0
129.0
2000.0
2000.0
130.0
2000.0
2000.0
131.0
2000.0
2000.0
132.0
-500.0
133.0
2000.0
2000.0
134.0
2000.0
2000.0
135.0
2000.0
2000.0
136.0
2000.0
2000.0
137.0
2000.0
2000.0
138.0
2000.0
2000.0
139.0
2000.0
2000.0
140.0
2000.0
2000.0
141.0
2000.0
2000.0
142.0
2000.0
2000.0
143.0
2000.0
2000.0
144.0
2000.0
176800.0
178800.0
0.05
0.1
0.15000000000000002
0.2
0.25
0.3
0.35
0.39999999999999997
0.44999999999999996
0.49999999999999994
0.5499999999999999
0.6
20.408163265306598
9.0157776108191
2.8766335168895694
0.0
-0.9600000000000364
-0.9103322712792306
-0.4572473708275311
1.1368683772161603E-13
0.20501045553317
0.0
-0.7049108791245544
-1.9531250000002274
Example: ERR
Example 7.6
MARR =
0.15
IRR =
0.1333
i" =
0.0747
MARR =
0.0747
ERR =
0.14
t
Net Cash
Rt
Ct
Period
Costs
Revenues
Net Cash
-110000.0
1.0
20000.0
20000.0
2.0
20000.0
20000.0
3.0
20000.0
20000.0
NPV =
7478.317090860985
7478.354020803944
4.0
20000.0
20000.0
MIRR =
0.09096703612464818
5.0
20000.0
20000.0
=MIRR(B4:B7,B2,D2)
6.0
20000.0
20000.0
7.0
20000.0
20000.0
8.0
20000.0
20000.0
9.0
20000.0
20000.0
Example 7.6
Example 7.6
10.0
30000.0
30000.0
i" =
0.1684
MARR =
0.2
i" =
0.2111
MARR =
0.2
NPV =
110000.0
102847.21957830325
-30.28998388045875
t
Net Cash
Rt
Ct
t
Net Cash
Rt
Ct
NFW =
407794.3445530428
416074.3647610544
-105.86390990577443
IRR =
0.13323269845647548
=IRR(F6:F16,0.1)
MIRR =
0.14229382044331174
=MIRR(F6:F16,0.1,D3)
NPV =
5935.185185185186
6361.3123445528545
NPV =
5935.185185185186
5935.21158742453
MIRR =
0.1725834601969538
MIRR =
0.1999982206343882
=MIRR(B4:B7,B2,D2)
=MIRR(B4:B7,B2,D2)
Mortgage
Interest
0.09
Years
30.0
Loan
85000.0
Payment
-683.9292244030638
Balance
Balance
Month
Start
Interest
Principle
End
1.0
85000.0
637.5
46.42922440306381
84953.57077559693
2.0
84953.57077559693
637.151780816977
46.77744358608686
84906.79333201084
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
84.0
85.0
86.0
87.0
88.0
89.0
90.0
91.0
92.0
93.0
94.0
95.0
96.0
97.0
98.0
99.0
100.0
101.0
102.0
103.0
104.0
105.0
106.0
107.0
108.0
109.0
110.0
111.0
112.0
113.0
114.0
115.0
116.0
117.0
118.0
119.0
120.0
121.0
122.0
123.0
124.0
125.0
126.0
127.0
128.0
129.0
130.0
131.0
132.0
133.0
134.0
135.0
136.0
137.0
138.0
139.0
140.0
141.0
142.0
143.0
144.0
145.0
146.0
147.0
148.0
149.0
150.0
151.0
152.0
153.0
154.0
155.0
156.0
157.0
158.0
159.0
160.0
161.0
162.0
163.0
164.0
165.0
166.0
167.0
168.0
169.0
170.0
171.0
172.0
173.0
174.0
175.0
176.0
177.0
178.0
179.0
180.0
181.0
182.0
183.0
184.0
185.0
186.0
187.0
188.0
189.0
190.0
191.0
192.0
193.0
194.0
195.0
196.0
197.0
198.0
199.0
200.0
201.0
202.0
203.0
204.0
205.0
206.0
207.0
208.0
209.0
210.0
211.0
212.0
213.0
214.0
215.0
216.0
217.0
218.0
219.0
220.0
221.0
222.0
223.0
224.0
225.0
226.0
227.0
228.0
229.0
230.0
231.0
232.0
233.0
234.0
235.0
236.0
237.0
238.0
239.0
240.0
241.0
242.0
243.0
244.0
245.0
246.0
247.0
248.0
249.0
250.0
251.0
252.0
253.0
254.0
255.0
256.0
257.0
258.0
259.0
260.0
261.0
262.0
263.0
264.0
265.0
266.0
267.0
268.0
269.0
270.0
271.0
272.0
273.0
274.0
275.0
276.0
277.0
278.0
279.0
280.0
281.0
282.0
283.0
284.0
285.0
286.0
287.0
288.0
289.0
290.0
291.0
292.0
293.0
294.0
295.0
296.0
297.0
298.0
299.0
300.0
301.0
302.0
303.0
304.0
305.0
306.0
307.0
308.0
309.0
310.0
311.0
312.0
313.0
314.0
315.0
316.0
317.0
318.0
319.0
320.0
321.0
322.0
323.0
324.0
325.0
326.0
327.0
328.0
329.0
330.0
331.0
332.0
333.0
334.0
335.0
336.0
337.0
338.0
339.0
340.0
341.0
342.0
343.0
344.0
345.0
346.0
347.0
348.0
349.0
350.0
351.0
352.0
353.0
354.0
355.0
356.0
357.0
358.0
359.0
360.0
Mortgage
Interest
0.09
Years
30.0
Loan
85000.0
Payment
-683.9292244030638
Balance
Balance
Month
Start
Interest
Principle
End
1.0
85000.0
637.5
46.42922440306381
84953.57077559693
2.0
84953.57077559693
637.151780816977
46.77744358608686
84906.79333201084
3.0
84906.79333201084
636.8009499900812
47.12827441298259
84859.66505759786
4.0
84859.66505759786
636.4474879319839
47.4817364710799
84812.18332112678
5.0
84812.18332112678
636.0913749084508
47.83784949461301
84764.34547163217
6.0
84764.34547163217
635.7325910372413
48.19663336582255
84716.14883826635
7.0
84716.14883826635
635.3711162869976
48.55810811606625
84667.59073015029
8.0
84667.59073015029
635.0069304761272
48.92229392693662
84618.66843622335
9.0
84618.66843622335
634.6400132716751
49.2892111313887
84569.37922509197
10.0
84569.37922509197
634.2703441881897
49.6588802148741
84519.72034487709
11.0
84519.72034487709
633.8979025865782
50.031321816485615
84469.68902306061
12.0
84469.68902306061
633.5226676729545
50.40655673010929
84419.2824663305
13.0
84419.2824663305
633.1446184974787
50.78460590558507
84368.4978604249
14.0
84368.4978604249
632.7637339531867
51.1654904498771
84317.33236997503
15.0
84317.33236997503
632.3799927748126
51.549231628251164
84265.78313834679
16.0
84265.78313834679
631.9933735376009
51.93585086546295
84213.84728748132
17.0
84213.84728748132
631.6038546561098
52.32536974695404
84161.52191773437
18.0
84161.52191773437
631.2114143830078
52.71781002005605
84108.80410771431
19.0
84108.80410771431
630.8160308078574
53.11319359520644
84055.69091411911
20.0
84055.69091411911
630.4176818558933
53.51154254717051
84002.17937157194
21.0
84002.17937157194
630.0163452867895
53.912879116274325
83948.26649245566
22.0
83948.26649245566
629.6119986934174
54.317225709646436
83893.94926674601
23.0
83893.94926674601
629.2046195005951
54.72460490246874
83839.22466184355
24.0
83839.22466184355
628.7941849638265
55.13503943923729
83784.08962240431
25.0
83784.08962240431
628.3806721680323
55.54855223503148
83728.54107016927
26.0
83728.54107016927
627.9640580262695
55.965166376794286
83672.57590379249
27.0
83672.57590379249
627.5443192784436
56.38490512462022
83616.19099866787
28.0
83616.19099866787
627.1214324900089
56.80779191305487
83559.3832067548
29.0
83559.3832067548
626.695374050661
57.23385035240278
83502.1493564024
30.0
83502.1493564024
626.266120173018
57.66310423004586
83444.48625217236
31.0
83444.48625217236
625.8336468912927
58.095577511771126
83386.39067466058
32.0
83386.39067466058
625.3979300599543
58.531294343109494
83327.85938031747
33.0
83327.85938031747
624.958945352381
58.97027905068285
83268.88910126679
34.0
83268.88910126679
624.5166682595009
59.41255614356294
83209.47654512322
35.0
83209.47654512322
624.0710740884241
59.858150314639715
83149.61839480858
36.0
83149.61839480858
623.6221379610644
60.307086441999445
83089.31130836658
37.0
83089.31130836658
623.1698348127494
60.75938959031441
83028.55191877627
38.0
83028.55191877627
622.714139390822
61.21508501224184
82967.33683376403
39.0
82967.33683376403
622.2550262532302
61.674198149833614
82905.6626356142
40.0
82905.6626356142
621.7924697671064
62.13675463595746
82843.52588097824
41.0
82843.52588097824
621.3264441073368
62.60278029572703
82780.92310068251
42.0
82780.92310068251
620.8569232551189
63.07230114794493
82717.85079953457
43.0
82717.85079953457
620.3838809965092
63.54534340655459
82654.30545612802
44.0
82654.30545612802
619.9072909209601
64.02193348210369
82590.28352264591
45.0
82590.28352264591
619.4271264198443
64.50209798321953
82525.7814246627
46.0
82525.7814246627
618.9433606849701
64.9858637180937
82460.7955609446
47.0
82460.7955609446
618.4559667070845
65.47325769597933
82395.32230324863
48.0
82395.32230324863
617.9649172743647
65.96430712869915
82329.35799611993
49.0
82329.35799611993
617.4701849708994
66.45903943216445
82262.89895668776
50.0
82262.89895668776
616.9717421751582
66.95748222790564
82195.94147445985
51.0
82195.94147445985
616.4695610584489
67.45966334461491
82128.48181111523
52.0
82128.48181111523
615.9636135833642
67.96561081969958
82060.51620029553
53.0
82060.51620029553
615.4538715022164
68.47535290084738
81992.04084739469
54.0
81992.04084739469
614.9403063554602
68.98891804760365
81923.05192934709
55.0
81923.05192934709
614.4228894701031
69.50633493296073
81853.54559441413
56.0
81853.54559441413
613.901591958106
70.02763244495782
81783.51796196918
57.0
81783.51796196918
613.3763847147687
70.55283968829508
81712.96512228088
58.0
81712.96512228088
612.8472384171065
71.08198598595732
81641.88313629491
59.0
81641.88313629491
612.3141235222118
71.61510088085197
81570.26803541406
60.0
81570.26803541406
611.7770102656054
72.15221413745837
81498.1158212766
61.0
81498.1158212766
611.2358686595745
72.69335574348929
81425.42246553312
62.0
81425.42246553312
610.6906684914984
73.23855591156541
81352.18390962156
63.0
81352.18390962156
610.1413793221617
73.78784508090212
81278.39606454065
64.0
81278.39606454065
609.5879704840548
74.34125391900898
81204.05481062164
65.0
81204.05481062164
609.0304110796623
74.89881332340155
81129.15599729825
66.0
81129.15599729825
608.4686699797369
75.46055442332693
81053.69544287493
67.0
81053.69544287493
607.902715821562
76.02650858150184
80977.66893429343
68.0
80977.66893429343
607.3325170072006
76.59670739586318
80901.07222689757
69.0
80901.07222689757
606.7580417017317
77.1711827013321
80823.90104419623
70.0
80823.90104419623
606.1792578314718
77.74996657159204
80746.15107762464
71.0
80746.15107762464
605.5961330821848
78.33309132087902
80667.81798630377
72.0
80667.81798630377
605.0086348972783
78.92058950578553
80588.89739679798
73.0
80588.89739679798
604.4167304759849
79.51249392707894
80509.38490287091
74.0
80509.38490287091
603.8203867715318
80.10883763153197
80429.27606523938
75.0
80429.27606523938
603.2195704892953
80.70965391376853
80348.5664113256
76.0
80348.5664113256
602.614248084942
81.31497631812181
80267.25143500748
77.0
80267.25143500748
602.0043857625561
81.92483864050769
80185.32659636697
78.0
80185.32659636697
601.3899494727523
82.53927493031154
80102.78732143666
79.0
80102.78732143666
600.7709049107749
83.15831949228891
80019.62900194437
80.0
80019.62900194437
600.1472175145827
83.78200688848108
79935.8469950559
81.0
79935.8469950559
599.5188524629192
84.41037194014461
79851.43662311575
82.0
79851.43662311575
598.885774673368
85.0434497296958
79766.39317338605
83.0
79766.39317338605
598.2479488003954
85.68127560266839
79680.71189778339
84.0
79680.71189778339
597.6053392333754
86.32388516968842
79594.3880126137
85.0
79594.3880126137
596.9579100946027
86.97131430846116
79507.41669830523
86.0
79507.41669830523
596.3056252372892
87.62359916577464
79419.79309913945
87.0
79419.79309913945
595.6484482435459
88.28077615951793
79331.51232297994
88.0
79331.51232297994
594.9863424223495
88.94288198071433
79242.56944099923
89.0
79242.56944099923
594.3192708074943
89.60995359556955
79152.95948740366
90.0
79152.95948740366
593.6471961555275
90.28202824753635
79062.67745915613
91.0
79062.67745915613
592.970080943671
90.95914345939286
78971.71831569674
92.0
78971.71831569674
592.2878873677255
91.64133703533832
78880.0769786614
93.0
78880.0769786614
591.6005773399605
92.32864706310329
78787.7483315983
94.0
78787.7483315983
590.9081124869872
93.02111191607662
78694.72721968222
95.0
78694.72721968222
590.2104541476166
93.71877025544723
78601.00844942676
96.0
78601.00844942676
589.5075633707007
94.42166103236309
78506.5867883944
97.0
78506.5867883944
588.799400912958
95.12982349010576
78411.4569649043
98.0
78411.4569649043
588.0859272367821
95.84329716628167
78315.61366773801
99.0
78315.61366773801
587.3671025080351
96.56212189502867
78219.05154584299
100.0
78219.05154584299
586.6428865938224
97.28633780924145
78121.76520803374
101.0
78121.76520803374
585.913239060253
98.01598534281084
78023.74922269094
102.0
78023.74922269094
585.178119170182
98.75110523288186
77924.99811745806
103.0
77924.99811745806
584.4374858809355
99.49173852212834
77825.50637893593
104.0
77825.50637893593
583.6912978420195
100.23792656104433
77725.26845237488
105.0
77725.26845237488
582.9395133928116
100.98971101025222
77624.27874136463
106.0
77624.27874136463
582.1820905602348
101.74713384282904
77522.5316075218
107.0
77522.5316075218
581.4189870564135
102.51023734665034
77420.02137017515
108.0
77420.02137017515
580.6501602763136
103.2790641267502
77316.7423060484
109.0
77316.7423060484
579.875567295363
104.05365710770081
77212.6886489407
110.0
77212.6886489407
579.0951648670552
104.83405953600857
77107.8545894047
111.0
77107.8545894047
578.3089094205352
105.62031498252861
77002.23427442217
112.0
77002.23427442217
577.5167570581663
106.41246734489755
76895.82180707727
113.0
76895.82180707727
576.7186635530795
107.21056084998429
76788.61124622729
114.0
76788.61124622729
575.9145843467046
108.01464005635921
76680.59660617093
115.0
76680.59660617093
575.104474546282
108.82474985678186
76571.77185631415
116.0
76571.77185631415
574.2882889223562
109.64093548070764
76462.13092083344
117.0
76462.13092083344
573.4659819062508
110.463242496813
76351.66767833663
118.0
76351.66767833663
572.6375075875247
111.29171681553908
76240.37596152109
119.0
76240.37596152109
571.8028197114081
112.1264046916557
76128.24955682943
120.0
76128.24955682943
570.9618716762207
112.96735272684316
76015.28220410258
121.0
76015.28220410258
570.1146165307694
113.81460787229446
75901.46759623029
122.0
75901.46759623029
569.2610069717272
114.66821743133664
75786.79937879895
123.0
75786.79937879895
568.4009953409922
115.52822906207166
75671.27114973689
124.0
75671.27114973689
567.5345336230266
116.3946907800372
75554.87645895685
125.0
75554.87645895685
566.6615734421763
117.26765096088752
75437.60880799596
126.0
75437.60880799596
565.7820660599697
118.14715834309413
75319.46164965286
127.0
75319.46164965286
564.8959623723964
119.0332620306674
75200.42838762219
128.0
75200.42838762219
564.0032129071664
119.92601149589746
75080.50237612629
129.0
75080.50237612629
563.1037678209472
120.82545658211666
74959.67691954417
130.0
74959.67691954417
562.1975768965813
121.73164750648255
74837.94527203769
131.0
74837.94527203769
561.2845895402826
122.64463486278123
74715.3006371749
132.0
74715.3006371749
560.3647547788117
123.56446962425207
74591.73616755065
133.0
74591.73616755065
559.4380212566299
124.49120314643392
74467.24496440422
134.0
74467.24496440422
558.5043372330316
125.4248871700322
74341.8200772342
135.0
74341.8200772342
557.5636505792564
126.36557382380738
74215.4545034104
136.0
74215.4545034104
556.615908775578
127.31331562748585
74088.14118778291
137.0
74088.14118778291
555.6610589083717
128.26816549469208
73959.87302228821
138.0
73959.87302228821
554.6990476671616
129.2301767359022
73830.64284555231
139.0
73830.64284555231
553.7298213416424
130.19940306142144
73700.4434424909
140.0
73700.4434424909
552.7533258186817
131.17589858438214
73569.26754390652
141.0
73569.26754390652
551.7695065792989
132.15971782376494
73437.10782608275
142.0
73437.10782608275
550.7783086956206
133.15091570744323
73303.9569103753
143.0
73303.9569103753
549.7796768278148
134.14954757524902
73169.80736280006
144.0
73169.80736280006
548.7735552210004
135.15566918206343
73034.651693618
145.0
73034.651693618
547.759887702135
136.16933670092885
72898.48235691707
146.0
72898.48235691707
546.738617676878
137.19060672618582
72761.29175019088
147.0
72761.29175019088
545.7096881264316
138.2195362766322
72623.07221391425
148.0
72623.07221391425
544.6730416043569
139.25618279870696
72483.81603111554
149.0
72483.81603111554
543.6286202333665
140.3006041696973
72343.51542694584
150.0
72343.51542694584
542.5763657020938
141.35285870097005
72202.16256824488
151.0
72202.16256824488
541.5162192618366
142.41300514122725
72059.74956310366
152.0
72059.74956310366
540.4481217232774
143.48110267978643
71916.26846042387
153.0
71916.26846042387
539.372013453179
144.55721094988485
71771.71124947398
154.0
71771.71124947398
538.2878343710548
145.64139003200899
71626.06985944198
155.0
71626.06985944198
537.1955239458149
146.73370045724891
71479.33615898473
156.0
71479.33615898473
536.0950211923855
147.8342032106783
71331.50195577406
157.0
71331.50195577406
534.9862646683054
148.94295973475846
71182.5589960393
158.0
71182.5589960393
533.8691924702947
150.0600319327691
71032.49896410653
159.0
71032.49896410653
532.743742230799
151.18548217226487
70881.31348193427
160.0
70881.31348193427
531.609851114507
152.3193732885568
70728.99410864571
161.0
70728.99410864571
530.4674558148428
153.46176858822105
70575.53234005749
162.0
70575.53234005749
529.3164925504311
154.6127318526327
70420.91960820486
163.0
70420.91960820486
528.1568970615364
155.77232734152744
70265.14728086333
164.0
70265.14728086333
526.988604606475
156.94061979658886
70108.20666106674
165.0
70108.20666106674
525.8115499580005
158.11767444506336
69950.08898662167
166.0
69950.08898662167
524.6256673996626
159.30355700340124
69790.78542961828
167.0
69790.78542961828
523.4308907221371
160.49833368092675
69630.28709593735
168.0
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353.0
5291.29589757711
39.68471923182832
644.2445051712355
4647.051392405874
354.0
4647.051392405874
34.85288544304405
649.0763389600197
3997.9750534458544
355.0
3997.9750534458544
29.984812900843906
653.94441150222
3344.0306419436347
356.0
3344.0306419436347
25.08022981457726
658.8489945884866
2685.181647355148
357.0
2685.181647355148
20.13886235516361
663.7903620479002
2021.391285307248
358.0
2021.391285307248
15.16043463980436
668.7687897632594
1352.6224955439884
359.0
1352.6224955439884
10.144668716579913
673.7845556864839
678.8379398575045
360.0
678.8379398575045
5.0912845489312835
678.8379398541325
3.3719516068231314E-9
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0.0
Retirement
Inflation
0.03
Future Value
Interest
0.12
1786282.6195300852
Growth Rt.
0.03
Initial
400.0
Todays $
Years
30.0
735924.7879997855
Month
Annuity
FV
1.0
400.0
14237.481713934676
2.0
401.0
14131.757839821305
3.0
402.0025
14026.819043981044
4.0
403.00750624999995
13922.659496624748
5.0
404.01502501562493
13819.273411253771
6.0
405.02506257816395
13716.65504433852
7.0
406.0376252346093
13614.798694999374
8.0
407.05271929769583
13513.69870468997
9.0
408.07035109594005
13413.349456882865
10.0
409.09052697367986
13313.745376757499
11.0
410.11325329111406
13214.880930890484
12.0
411.13853642434185
13116.750626948227
13.0
412.16638276540266
13019.349013381778
14.0
413.19679872231615
12922.670679123998
15.0
414.2297907191219
12826.710253288917
16.0
415.2653651959197
12731.4624048734
17.0
416.30352860890946
12636.921842460972
18.0
417.34428743043173
12543.08331392785
19.0
418.3876481490078
12449.941606151153
20.0
419.4336172693803
12357.49154471934
21.0
420.48220131255374
12265.72799364469
22.0
421.5334068158351
12174.645855078024
23.0
422.58724033287467
12084.24006902546
24.0
423.6437084337068
11994.50561306735
25.0
424.7028177047911
11905.437502079221
26.0
425.76457474905305
11817.030787954875
27.0
426.82898618592566
11729.280559331444
28.0
427.89605865139043
11642.181941316607
29.0
428.9657987980189
11555.73009521772
30.0
430.0382132950139
11469.920218273035
31.0
431.11330882825143
11384.747543384869
32.0
432.19109210032207
11300.207338854781
33.0
433.27156983057284
11216.294908120708
34.0
434.3547487551493
11133.005589496053
35.0
435.4406356270371
11050.334755910684
36.0
436.5292372161047
10968.277814653922
37.0
437.62056030914493
10886.830207119361
38.0
438.7146117099178
10805.987408551644
39.0
439.81139823919256
10725.74492779507
40.0
440.9109267347905
10646.098307044118
41.0
442.01320405162744
10567.043121595767
42.0
443.1182370617565
10488.57497960372
43.0
444.22603265441086
10410.689521834383
44.0
445.3365977360469
10333.382421424722
45.0
446.449939230387
10256.649383641863
46.0
447.56606407846294
10180.486145644527
47.0
448.6849792386591
10104.888476246177
48.0
449.8066916867557
10029.852175679991
49.0
450.93120841597255
9955.37307536553
50.0
452.05853643701244
9881.447037677173
51.0
453.1886827781049
9808.069955714222
52.0
454.32165448505015
9735.23775307278
53.0
455.45745862126273
9662.946383619268
54.0
456.59610226781587
9591.19183126566
55.0
457.7375925234854
9519.970109746359
56.0
458.88193650479406
9449.277262396758
57.0
460.029141346056
9379.10936193341
58.0
461.1792141994211
9309.462510235888
59.0
462.3321622349196
9240.332838130174
60.0
463.4879926405069
9171.716505173761
61.0
464.6467126221081
9103.609699442271
62.0
465.8083294036634
9036.008637317702
63.0
466.9728502271725
8968.909563278212
64.0
468.1402823527404
8902.308749689511
65.0
469.3106330586223
8836.202496597754
66.0
470.4839096412688
8770.587131524013
67.0
471.6601194153719
8705.459009260217
68.0
472.8392697139103
8640.8145116667
69.0
474.0213678881951
8576.650047471154
70.0
475.20642130791555
8512.962052069142
71.0
476.39443736118534
8449.746987326054
72.0
477.5854234545883
8387.001341380563
73.0
478.7793870132247
8324.721628449517
74.0
479.97633548075777
8262.9043886343
75.0
481.17627631945965
8201.546187728598
76.0
482.3792170102583
8140.643617027643
77.0
483.5851650527839
8080.193293138824
78.0
484.79412796541584
8020.191857793735
79.0
486.0061132853294
7960.635977661603
80.0
487.22112856854267
7901.522344164115
81.0
488.439181389964
7842.847673291607
82.0
489.6602793434389
7784.60870542063
83.0
490.8844300417975
7726.802205132851
84.0
492.111641116902
7669.424961035331
85.0
493.3419202196942
7612.473785582097
86.0
494.5752750202434
7555.945514897083
87.0
495.81171320779396
7499.837008598341
88.0
497.0512424908134
7444.1451496236
89.0
498.29387059704044
7388.866844057086
90.0
499.539605273533
7333.9990209576545
91.0
500.78845428671684
7279.538632188165
92.0
502.0404254224336
7225.482652246173
93.0
503.2955264859897
7171.828078095829
94.0
504.5537653022046
7118.571929001059
95.0
505.8151497154601
7065.711246359962
96.0
507.07968758974874
7013.243093540457
97.0
508.3473868087231
6961.164555717135
98.0
509.6182552757449
6909.472739709336
99.0
510.8923009139342
6858.164773820404
100.0
512.169531666219
6807.237807678172
101.0
513.4499554953845
6756.689012076601
102.0
514.733580384123
6706.515578818607
103.0
516.0204143350833
6656.714720560053
104.0
517.310465370921
6607.283670654903
105.0
518.6037415343483
6558.219683001524
106.0
519.9002508881841
6509.520031890128
107.0
521.2000015154046
6461.182011851339
108.0
522.503001519193
6413.202937505907
109.0
523.809259022991
6365.580143415516
110.0
525.1187821705485
6318.310983934709
111.0
526.4315791259748
6271.392833063907
112.0
527.7476580737898
6224.823084303532
113.0
529.0670272189742
6178.599150509196
114.0
530.3896947870217
6132.718463747991
115.0
531.7156690239892
6087.178475155802
116.0
533.0449581965491
6041.976654795734
117.0
534.3775705920405
5997.1104915175465
118.0
535.7135145185206
5952.57749281816
119.0
537.0527983048169
5908.3751847031735
120.0
538.3954303005788
5864.501111549435
121.0
539.7414188763303
5820.952835968621
122.0
541.0907724235211
5777.727938671826
123.0
542.4434993545799
5734.8240183351545
124.0
543.7996081029663
5692.2386914663275
125.0
545.1591071232237
5649.969592272269
126.0
546.5220048910318
5608.014372527676
127.0
547.8883099032594
5566.370701444548
128.0
549.2580306780175
5525.036265542732
129.0
550.6311757547124
5484.008768521373
130.0
552.0077536940992
5443.285931131363
131.0
553.3877730783344
5402.865491048704
132.0
554.7712425110302
5362.745202748837
133.0
556.1581706173077
5322.92283738189
134.0
557.548566043851
5283.396182648856
135.0
558.9424374589606
5244.163042678691
136.0
560.339793552608
5205.221237906324
137.0
561.7406430364895
5166.568604951573
138.0
563.1449946440806
5128.202996498963
139.0
564.5528571306908
5090.122281178425
140.0
565.9642392735175
5052.324343446902
141.0
567.3791498717012
5014.8070834708105
142.0
568.7975977463805
4977.5684170093955
143.0
570.2195917407464
4940.606275298929
144.0
571.6451407200982
4903.918604937797
145.0
573.0742535718985
4867.503367772416
146.0
574.5069392058282
4831.358540784008
147.0
575.9432065538427
4795.482115976204
148.0
577.3830645702274
4759.872100263511
149.0
578.8265222316529
4724.526515360563
150.0
580.2735885372321
4689.443397672244
151.0
581.7242725085752
4654.620798184577
152.0
583.1785831898466
4620.056782356474
153.0
584.6365296478211
4585.749430012241
154.0
586.0981209719406
4551.696835234923
155.0
587.5633662743704
4517.897106260405
156.0
589.0322746900563
4484.348365372332
157.0
590.5048553767814
4451.048748797785
158.0
591.9811175152233
4417.996406603743
159.0
593.4610703090113
4385.189502594309
160.0
594.9447229847839
4352.626214208707
161.0
596.4320847922459
4320.304732420028
162.0
597.9231650042265
4288.223261634732
163.0
599.417972916737
4256.380019592889
164.0
600.9165178490288
4224.773237269179
165.0
602.4188091436513
4193.401158774605
166.0
603.9248561665104
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