My Math Forum present value question

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 April 9th, 2015, 07:24 AM #21 Newbie   Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 Abraham, if the offer is still open, do you have a formula for the future value of this too? A formula that would sum the total of each future payment.
April 9th, 2015, 07:37 AM   #22
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From: Rawalpindi, Punjab

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Quote:
 Originally Posted by cb123 Abraham, if the offer is still open, do you have a formula for the future value of this too? A formula that would sum the total of each future payment.
My offer is open-ended, like a perpetuity sort of forever young.

Yet as I make a living doing odd freelance jobs earning $100 biweekly same as the payments in your example yet such payments stay constant over the course of its life and annual inflation further erodes the present and future value of my earnings. And yesterday I received an email from my employer that my contract was suspended until I fix the figures for Annual Income of portfolios that we are analyzing for local governments (Cities and County Treasurers) across the vast American expanse excluding Alaska, Hawaii and Puerto Rico the latter a common wealth and not a member of the Socialist Union (circa early 21st century Fox Studios). Therefore expect a lag between my deliverance of the financial sermon that puts the worshipers in trance at the Sunday Mass of Earthly Beings who are shown the light divine. Sorry cb123, I got carried away. Would try to post the formula as soon as I finish my odd job to have my contract reinstated. Last edited by skipjack; April 9th, 2015 at 04:23 PM.  April 9th, 2015, 06:23 PM #23 Newbie Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 Completely understandable. The weight of the financial World rests squarely upon your shoulders. I shall wait patiently for a glimpse of the elusive preternatural equation. April 9th, 2015, 09:58 PM #24 Member Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5 Quote:  Originally Posted by cb123 Completely understandable. The weight of the financial World rests squarely upon your shoulders. I shall wait patiently for a glimpse of the elusive preternatural equation. Here is my version of unnatural wonders of finance Please find the formulas for present and future value an annuity with linear gradient where payment period and gradient periods are not the same Code: A=100 g=15 i=13% annual cpd biweekly n=3.5 years n_1=FLOOR(n)=3 n_2=n-FLOOR(n)= 3.5-3 = 0.5 c=1/26 biweekly interest compounding p=1/26 period is a biweek Find PV PV = (1 - x ^ (-1 / p)) / (x - 1) * ((A + g * n_1 - g) * (y ^ (n_1) - 1) / (y - 1) - g / (y - 1) * (((y) ^ (n_1) - 1) / (y - 1) - n_1)) + (A + g * n_1) * ((y) ^ (n_1)) * (1 - (x) ^ (-(n_2 / p))) / (x - 1) PV =$8,563.08

Find FV

FV = (x) ^ (n_2 / p) * ((x) ^ (1 / p) - 1) / (x - 1) * (A * ((z) ^ (n_1) - 1) / (z - 1) + g / (z - 1) * (((z) ^ (n_1) - 1) / (z - 1) - n_1)) + (A + g * n_1) * ((x) ^ (n_2 / p) - 1) / (x - 1)

FV = $13,481.60 aey(i,c) = (1 + i*c)^(1/c) - 1 i=0.13 c=1/26 aey(13%,1/26) = (1 + 0.13/26)^(26) - 1 aey(13%,1/26) = 0.138459553 aey(13%,1/26) = 13.85% x=(1 + aey(i,c))^p p=1/26 x=(1 + 13.85%)^(1/26) x=(1.1385)^(0.038462) x=1.005 y=(x)^(-1/p) y=(1.005)^(-26) y=0.87837991 z=(x)^(1/p) z=(1.005)^(26) z=1.13846 PV =$8,563.08

FV = $13,481.60  April 10th, 2015, 07:58 AM #25 Newbie Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 Abraham, I may not have explained what I was looking for (in fact I probably used the wrong term when I said Future Value) but I am trying to calculate the sum total of payments without interest. For example, in our scenario if$100 is paid every two weeks for the first year that is $2600, then the next year,$115 every two weeks = $2990, the third year($130 x 26) = $3380 and lastly the 1/2 year($145 x 13) = $1885 so the total paid is$10,855. Is there a formula for that one? Last edited by cb123; April 10th, 2015 at 08:09 AM.
April 10th, 2015, 08:10 AM   #26
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Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

Quote:
 Originally Posted by cb123 Abraham, I may not have explained what I was looking for (in fact I probably used the wrong term when I said Future Value) but I am trying to calculate the sum total of payments without interest. For example, in our scenerio if 100 is paid every two weeks for the first year that is 2600, then the next year, 115 every two weeks = 2990, the third year(130 x 26) = 3380 and lastly the 1/2 year(145 x 13) = 1885 so the total paid is 10,855. Is there a formula for that one?
I am pretty sure there is more than one formula to get the sum of such payments that earns no interest

Will return after a bit of sleep to refresh my body and mind to check if any new word of revelation has come down from heavens, if so then it will be made public

 April 10th, 2015, 08:51 AM #27 Newbie   Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 If chemicals are required for inspiration remember..... just a recreational dose.
April 10th, 2015, 08:56 AM   #28
Member

Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

Quote:
 Originally Posted by cb123 Abraham, I may not have explained what I was looking for (in fact I probably used the wrong term when I said Future Value) but I am trying to calculate the sum total of payments without interest. For example, in our scenario if 100 is paid every two weeks for the first year that is 2600, then the next year, 115 every two weeks = 2990, the third year(130 x 26) = 3380 and lastly the 1/2 year(145 x 13) = 1885 so the total paid is 10,855. Is there a formula for that one?
I suppose, the Lord heard my cry for guidance as I was bewildering in darkness of mid-day light and the word came down from heavens

Code:
A=100
G=15
n=3.5
n_1=FLOOR(n)=3
n_2=n-FLOOR(n)=0.5
p=1/26

S = (n_1 * A / p) + G/p * (n_1 * n_1 - 1)/2 + (A + n_1 * G) * n_2 / p
S = (3 * 100 * 26 ) + 15 * 26 * (3 * 3 - 1)/2 + (100 + 3 * 15) * 0.5 * 26

S = 7800 + 390 * (3 * 2)/2 + 145 * 13
S = 7800 + 390 * 3 + 1885
S = 7800 + 1170 + 1885

S = 10,855

 April 10th, 2015, 09:38 AM #29 Newbie   Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 Once again thank you!
 April 10th, 2015, 10:46 AM #30 Newbie   Joined: Apr 2015 From: miami Posts: 18 Thanks: 0 S = (n_1 * A / p) + G/p * (n_1 * n_1 - 1)/2 + (A + n_1 * G) * n_2 / p I think there needs to be a slight change in formula: S = (n_1 * A / p) + G/p * (n_1 * (n_1 - 1))/2 + (A + n_1 * G) * n_2 / p Is this correct?

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