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June 2nd, 2015, 08:49 PM   #11
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A perpetuity can not be paid off

Keeping the time horizon to 34 years with a present value of $2,558.14, here is the complete bank statement

Code:
N	Month	Payment	Intereest	Balance
0	0	 $-   	 $-   	 $2,558.14 
0.083333333	1	 $-   	 $4.26 	 $2,562.40 
1	13	 $(120.00)	 $51.16 	 $2,493.57 
2	25	 $(121.44)	 $49.87 	 $2,422.00 
3	37	 $(122.90)	 $48.44 	 $2,347.54 
4	49	 $(124.37)	 $46.95 	 $2,270.12 
5	61	 $(125.86)	 $45.40 	 $2,189.66 
6	73	 $(127.37)	 $43.79 	 $2,106.08 
7	85	 $(128.90)	 $42.12 	 $2,019.29 
8	97	 $(130.45)	 $40.39 	 $1,929.23 
9	109	 $(132.02)	 $38.58 	 $1,835.80 
10	121	 $(133.60)	 $36.72 	 $1,738.91 
11	133	 $(135.20)	 $34.78 	 $1,638.49 
12	145	 $(136.83)	 $32.77 	 $1,534.43 
13	157	 $(138.47)	 $30.69 	 $1,426.66 
14	169	 $(140.13)	 $28.53 	 $1,315.06 
15	181	 $(141.81)	 $26.30 	 $1,199.55 
16	193	 $(143.51)	 $23.99 	 $1,080.03 
17	205	 $(145.23)	 $21.60 	 $956.39 
18	217	 $(146.98)	 $19.13 	 $828.55 
19	229	 $(148.74)	 $16.57 	 $696.38 
20	241	 $(150.53)	 $13.93 	 $559.78 
21	253	 $-   	 $11.20 	 $570.97 
22	265	 $-   	 $11.42 	 $582.39 
23	277	 $-   	 $11.65 	 $594.04 
24	289	 $-   	 $11.88 	 $605.92 
25	301	 $-   	 $12.12 	 $618.04 
26	313	 $-   	 $12.36 	 $630.40 
27	325	 $-   	 $12.61 	 $643.01 
28	337	 $-   	 $12.86 	 $655.87 
29	349	 $-   	 $13.12 	 $668.99 
30	361	 $-   	 $13.38 	 $682.37 
31	373	 $-   	 $34.12 	 $716.48 
32	385	 $-   	 $35.82 	 $752.31 
32.5	391	 $(200.00)	 $18.81 	 $571.12 
33	397	 $(200.00)	 $14.28 	 $385.39 
33.5	403	 $(200.00)	 $9.63 	 $195.03 
34	409	 $(200.00)	 $4.88 	 $(0.10)
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June 2nd, 2015, 10:23 PM   #12
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Slight error in my Excel file corrected

Here is the same schedule again

Code:
N	Month	Payment	Interest	Balance
0	0	 $-   	 $-   	 $2,558.14 
0.083333333	1	 $-   	 $4.26 	 $2,562.40 
1	13	 $(120.00)	 $51.25 	 $2,493.65 
2	25	 $(121.44)	 $49.87 	 $2,422.08 
3	37	 $(122.90)	 $48.44 	 $2,347.63 
4	49	 $(124.37)	 $46.95 	 $2,270.21 
5	61	 $(125.86)	 $45.40 	 $2,189.75 
6	73	 $(127.37)	 $43.79 	 $2,106.17 
7	85	 $(128.90)	 $42.12 	 $2,019.39 
8	97	 $(130.45)	 $40.39 	 $1,929.33 
9	109	 $(132.02)	 $38.59 	 $1,835.90 
10	121	 $(133.60)	 $36.72 	 $1,739.02 
11	133	 $(135.20)	 $34.78 	 $1,638.59 
12	145	 $(136.83)	 $32.77 	 $1,534.54 
13	157	 $(138.47)	 $30.69 	 $1,426.76 
14	169	 $(140.13)	 $28.54 	 $1,315.17 
15	181	 $(141.81)	 $26.30 	 $1,199.66 
16	193	 $(143.51)	 $23.99 	 $1,080.14 
17	205	 $(145.23)	 $21.60 	 $956.51 
18	217	 $(146.98)	 $19.13 	 $828.66 
19	229	 $(148.74)	 $16.57 	 $696.50 
20	241	 $(150.53)	 $13.93 	 $559.90 
21	253	 $-   	 $11.20 	 $571.10 
22	265	 $-   	 $11.42 	 $582.52 
23	277	 $-   	 $11.65 	 $594.17 
24	289	 $-   	 $11.88 	 $606.06 
25	301	 $-   	 $12.12 	 $618.18 
26	313	 $-   	 $12.36 	 $630.54 
27	325	 $-   	 $12.61 	 $643.15 
28	337	 $-   	 $12.86 	 $656.01 
29	349	 $-   	 $13.12 	 $669.13 
30	361	 $-   	 $13.38 	 $682.52 
31	373	 $-   	 $34.13 	 $716.64 
32	385	 $-   	 $35.83 	 $752.47 
32.5	391	 $(200.00)	 $18.81 	 $571.29 
33	397	 $(200.00)	 $14.28 	 $385.57 
33.5	403	 $(200.00)	 $9.64 	 $195.21 
34	409	 $(200.00)	 $4.88 	 $0.09
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June 3rd, 2015, 04:40 AM   #13
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Quote:
Originally Posted by AbrahamA View Post
Code:
N	Month	Payment	Interest	Balance
0	0	 $-   	 $-   	 $2,558.14 
0.083333333	1	 $-   	 $4.26 	 $2,562.40 : NOTE#1
1	13	 $(120.00)	 $51.25 	 $2,493.65 
......
 
32	385	 $-   	 $35.83 	 $752.47 
32.5	391	 $(200.00)	 $18.81 	 $571.29 : NOTE#2
33	397	 $(200.00)	 $14.28 	 $385.57 
33.5	403	 $(200.00)	 $9.64 	 $195.21 
34	409	 $(200.00)	 $4.88 	 $0.09
NOTE#1 : I presume that's your interpretation of "deferred 1 month".
(don't you think it's silly to delay a 34 years thing by 1 month?!)

NOTE#2: your interest calculations from this point are incorrect:
rate should be the semiannual equivalent, thus .024695, not .025

We are evidently not interpreting Anna's gibberish the same way,
so I quit, and leave this in your EXCELlent hands.

It is now up to YOU to show dear Anna how to arrive at the proper
amount after 34 years (or is it 34 years and 1 month!), such amount
to permit a perpetual (never ending) annuity starting at 200 euros
annually, and increasing by a constant 7 euros annually.
(something I'd never heard of before, and had to humbly PM
Sir Jonah for his explanation of this, which he promptly delayed
with the excuse of a violent hangover that had to be sleeped off).

Who knows: Anna may be impressed...and rich... and accept your
marriage proposal...

Last edited by Denis; June 3rd, 2015 at 05:06 AM.
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June 3rd, 2015, 05:11 AM   #14
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I would return to Anna's mansion after the weekend as have to sort out couple of freelancing projects that help me buy certain items I need daily such as Coke (soft drink) and a pack of tobacco.
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June 3rd, 2015, 09:42 AM   #15
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Warning: Beer soaked ramblings follow.

Quote:
Originally Posted by Anna View Post
Consider a perpetuity deferred of 1 month and whose payments are: annual and variable as a geometrical progression (first term 120 euros and ratio 1.2) in the first 20 years, no payments in the next 12 years, semestral and constant payments of 200 euros in the next 2 years and annual and variable as an arithmetical progression (ratio 7 years) in the following period. Compute the present value of the perpetuity if the annual interest rate is 2% in the first 30 years and 5% in the following period.

Thank you!
As I wrote in the beginning, before you two eager (caffeine and coke stimulated) non-alcoholic beverage drinkers went elbow deep into this (no work shown) problem: What have you tried so far?

Last edited by jonah; June 3rd, 2015 at 09:48 AM.
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June 3rd, 2015, 11:16 AM   #16
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Quote:
Originally Posted by jonah View Post
......What have you tried so far?
Ya...and get more Italian infested English...
Anyway, Abe's the one who disobeyed you first
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June 3rd, 2015, 09:42 PM   #17
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Quote:
Originally Posted by jonah View Post
before you two eager (caffeine and coke stimulated) non-alcoholic beverage drinkers went elbow deep into this
I thought we were knee deep into this.

Three Amigos fighting over a A Fistful of Dollars yet The Last Man Standing out of The Good, The Bad and the Ugly will take home The Lady or the Loot Laughing All the Way to the Bank of Canada.

We may not have understood the message sent by our Lady Anna as we see contradictory gradients in PV calculations of Grand Daddy Denis and that of Abe from Yonkers a bit Bonkers.

Yet if we were to accept Abe's assumptions about the series of cash flows and its timinings then Abe will stand the challenge to demonstrate that the present value of $5,637.87 computed by summing up each PV is indeed right on the German Mark.

PV = PV_1 + PV_2 + PV_3 + PV_4
PV = 2,182 + 0 + 376.14 + 3079.73
PV = 5,637.87

So my Los Amigos, Nevada.

What's the bet on the table?
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June 4th, 2015, 04:49 AM   #18
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Ok, accepting your assumptions (including the compounding semi-annually
instead of annually during years 33 and 34 and the strange 1 month waiting
period at the beginning...presumably for Lady Anna to bathe vigorously
and get a combo manicure-pedicure), please show us:

1: clearly what those assumptions are (now disguised within Excel coding)

2: what amount will be in the "account" 1+34*12 = 409 months later

3: WHY this amount accommodates a perpetual annuity of:
"200 euros at end of month 409+12=421, then constant increases of
7 euros annually (i.e. 207, 214, 221...) until kingdom cometh...

Yours truly thanketh thee in advance.

In the meantime, I will post (title "Short Annuity") a similar problem
for your entertainment.
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June 4th, 2015, 08:18 AM   #19
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Please have a view of the Excel sheet that shows the present value of three separate annuities

https://www.dropbox.com/s/7bg397tqb0d2f62/npv.xlsx?dl=0

A) First annuity with geometric gradient
B) A plus annuity with constant payments
C) B plus perpetuity with linear gradient

For A and B the balance at the end of 20 years and 34 years respectively come to a naught (0)

For C, this is a never ending money making scheme whose present value can be determined however its future value tends to infinity that can never be paid off. Sort of like the U.S. public debt in the hands of unfriendly foes from Far East

As for your Short Annuity, I noticed a new thread with the same title posted by you. I have not opened the thread as have some other tasks to complete that earn me 50 dollars a week down from what I was making in March 200 dollars a week so that is also an example of an annnuity with linear gradient albeit it a diminishing one

In closing as overheard on New York TV show, its not how long it is but it's how you use it. Short annuity that is.
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June 4th, 2015, 10:56 AM   #20
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Ahhh...thanks for that link...now 100% clear.
I matched it to the penny using my trusty UBasic;
Excel is a headache, probably invented in Punjab.

AND as you previously enunciated brandishing your index finger,
you were correct using the questionable assumptions you made

The required end of 34th year amount of ~6,800 is quite higher
than the 4,000 required if the annuity did not increase by 7,
which is all in the Bank's favor...what else is new!

I showed your work to a local financial firm and they asked me
to offer you (on their behalf) 51dollars per week, and would have
offered 55 dollars per week had your assumptions been as good as
mine(!)...AND they will not pay your moving expenses

Last edited by Denis; June 4th, 2015 at 10:59 AM.
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