# A math question



## pnky (Jul 16, 2012)

If I invested $100 a month every month for a year and at the end of the year I have $1240 - what is my net rate of return ? 

It wont be as simple as (1240-1200)/1200 right since not all installments have been there for the same time.


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## FrugalTrader (Oct 13, 2008)

Easiest way is to use XIRR with spreadsheet software. Here is a post that I wrote with some instructions:
http://www.milliondollarjourney.com/how-to-calculate-annual-investment-returns-using-xirr.htm


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## pnky (Jul 16, 2012)

FrugalTrader said:


> Easiest way is to use XIRR with spreadsheet software. Here is a post that I wrote with some instructions:
> http://www.milliondollarjourney.com/how-to-calculate-annual-investment-returns-using-xirr.htm


Thank you


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## Robillard (Apr 11, 2009)

By my calculations, I estimate that pnky has earned a nominal return (compounded monthly) of 7.13%. This is equivalent to an effective annual rate (with one compound period in a year) of 7.37%. Someone please double check.


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## crazyjackcsa (Aug 8, 2010)

I ended up with 6.04%.


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## HaroldCrump (Jun 10, 2009)

6.22%, assuming each contribution is made on the 1st of every month and the calculation date is 12/31.


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## Cal (Jun 17, 2009)

Yeah, I got 6.22% as well. But I just calculated it in my head, no spreadsheet for me. :biggrin:


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## Toronto.gal (Jan 8, 2010)

LOL, now 4 different answers.

I got 6.12% using the compound interest formulas.

So, who is right? :confused2:


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## none (Jan 15, 2013)

Alternatively, I get 0.59% per month or 6.9% per year.

=RATE(1*12,-100,0,1240)

=1-(1-A1)^12


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## Robillard (Apr 11, 2009)

I think my answer assumed that all contributions were made at the end of the month. That would explain some of the discrepancy between my answer, and the ones that found a return of about 6%.


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## Addy (Mar 12, 2010)

Are there any calculators where you can enter your taxation rates and calculate your after tax rate of return?


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## Ponderling (Mar 1, 2013)

good old HP 12C was the financial variant, of my trusty old enginnering based HP11C, I recall.

I also have a hp27s (i think that is the number), and there was a 28 financuial variant as well. 

I am not a smart phone owner, but I am sure by now there is a program, um, the young ones now call them apps, that will solve the present value, future value or internal rate of return of a stream of income.


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## GoldStone (Mar 6, 2011)

Addy said:


> Are there any calculators where you can enter your taxation rates and calculate your after tax rate of return?


Excel, OpenOffice or Google Sheets. 

Use XIRR function to calculate your rate of return before tax. Apply the tax rate to the XIRR result to calculate the after-tax RoR.


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## FinancialEngineer (May 28, 2013)

*There are more than one interest rates for your investment*



pnky said:


> If I invested $100 a month every month for a year and at the end of the year I have $1240 - what is my net rate of return ?
> 
> It wont be as simple as (1240-1200)/1200 right since not all installments have been there for the same time.


The answer to your question requires knowing the compounding frequency on interest whether the savings account is paying you interest on annual basis, quarterly basis, monthly basis, fortnightly basis, weekly basis, daily basis or continuous (infinite) basis.

Use of XIRR is only required when you have a date schedule for your cash flows. The payments may be periodic but the XIRR calculation in Excel or other software will use a Actual/365 day count basis.

If the payments are periodic then the Excel RATE function (that is programmed on the basis of TVM equation) will return a periodic interest rate that is calculated on the basis of 30/360 day count.

So there is not one rate that would be the answer to your question. I can post back later when I run the numbers through the Excel software I use to report various interest rates where different frequencies of interest compounding is used.


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## MoneyGal (Apr 24, 2009)

Great first post, Financial Engineer!!! :encouragement:


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## FinancialEngineer (May 28, 2013)

*RATE in Excel*



MoneyGal said:


> Great first post, Financial Engineer!!! :encouragement:


You have a periodic payment of $100 for 12 periods (months) that has a terminal value of $1240 and you would like to find the interest rate

In terms of finance, the equation to use would be

FVA = [{(1+i)^n} - 1]/i

this equation is used when payments/deposits are made at end of period (month in this case)

If the payments/deposits are made at start of period (month in this case) then the following equation is used instead

FVAD = (i+i)[{(1+i)^n} - 1]/i

Now using Excel RATE function you can find your periodic rate (monthly nominal rate). Excel TVM calculations make use of following equation

*FV* (1+RATE)^-NPER + *PMT* _(1+RATE*type)_*[ 1 - {(1+RATE)^-NPER} ]/RATE + *PV* = 0

Solving for RATE in the three equations is not possible with algebraic manipulation. Thus Excel and other programs employ numerical methods, this is one of the reasons that Excel RATE asks for a guess which defaults to 10% when omitted

If the monthly deposits were at the start of month which is usually the case with savings deposits then Excel RATE gives you the following results

NPER	12
PMT	-100
PV	0
FV	1240
TYPE	1

*=RATE(*12, -100, 0, 1240, *1)*
*RATE 0.503%*

=RATE(12, -100, 0, 1240, 1)* * 12*
*Annual Rate 6.041%*

*=EFFECT(* RATE(12, -100, 0, 1240, 1) * 12*, 12)*
*AEY 6.211%*

But if the monthly deposits were at the end of the month then the following results are returned by Excel RATE function

NPER	12
PMT	-100
PV	0
FV	1240
TYPE	0

*=RATE(*12, -100, 0, 1240,* 0)*
*RATE 0.594%*

*=RATE(*12, -100, 0, 1240, 0)* * 12*
*Annual Rate 7.130%*

*=EFFECT( *RATE(12, -100, 0, 1240, 0) * 12,* 12)*
*AEY 7.367%*

Now if you think, this is fun then wait for my next post that will highlight the limited functionality of Excel functions and how you can overcome such shortcomings of Excel to find a variety of interest rates.


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## MoneyGal (Apr 24, 2009)

I do...think this is fun. I worked at the Fields Institute for a while, yo.


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## FinancialEngineer (May 28, 2013)

*Get me a rate, any one. I don't care which one. Just get me a rate*



MoneyGal said:


> I do...think this is fun. I worked at the Fields Institute for a while, yo.


We will now get to see various different interest rates for this investment where a $100 is deposited at the start of each month for 12 months leading to a future terminal value of $1,240

The following are the values that are required to use this particular Excel RATE function that finds interest rate for almost any sort of interest compounding. But this is just a part of what else may be done by using this RATE function discussion of which is beyond the scope of this OP question


GRADIENT0%TAXRATE0%NPER12PMT-100PV0FV1240TYPE1GTYPE0COMPOUNDING1PERIOD1DISTRIBUTION1GTYPE1RATE?

Here is the periodic (monthly) interest rate which is the same one as reported by Excel RATE function

*=tadRATE*(0%, 0%, 12, -100, 0, 1240, 1, 0, , 1, 1, 1, 1)
*0.503%
*
But now we will change things around and tell tadRATE function that our period is a MONTH. We will do this by giving a value of 1/12 to the variable called PERIOD

*=tadRATE(*0%, 0%, 12, -100, 0, 1240, 1, 0, , 1, *1/12,* 1, 1)
*AEY 6.211%*

As you noticed this value is the AEY (annual effective yield) and an annual nominal rate may be found by using tadNOMINAL function as follows

*=tadNOMINAL( *tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , 1, 1/12, 1, 1), *1/12)*
*Annual nominal rate 6.041%*

These were the result when we have an annual compounding of interest for monthly deposits. The following are the many different rate of interest that result from making use of various compounding frequencies of interest

*Semi-Annual* Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *6/12,* 1/12, 1, 1)
*AEY 6.11746%*

*Quarterly* Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *3/12,* 1/12, 1, 1)
*AEY 6.07139%*

*Monthly *Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/12,* 1/12, 1, 1)
*AEY 6.04092%*

*Fortnightly* Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/26,* 1/12, 1, 1)
*AEY 6.03276%*

*Weekly *Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/52,* 1/12, 1, 1)
*AEY 6.02926%*

*Daily *Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/365,* 1/12, 1, 1)
A*EY 6.02627%*

*Hourly *Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/8760,* 1/12, 1, 1)
*AEY 6.02579%*

*Minutely* Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/525600,* 1/12, 1, 1)
*AEY 6.0257702%*

*Secondly *Compounding
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *1/31536000, *1/12, 1, 1)
*AEY 6.0257699%*

*Infinite (continuous) *compounding of interest
=tadRATE(0%, 0%, 12, -100, 0, 1240, 1, 0, , *0,* 1/12, 1, 1)
*AEY 6.02576987%*

I thought I asked him for a single rate and he gave me a bunch. 

And why would one want Hourly, Minutely or Secondly compounding of interest to find the rate. Well this is internet age and companies like Google earn $2,000 per second and companies like Amazon sell in amount of $10,000 per second on average. So I am pretty sure they are investing part of such income immediately into funds that offer returns in excess of investment


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## humble_pie (Jun 7, 2009)

i think it's fun. I may not understand but i've always been a sacher torte.


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## Robillard (Apr 11, 2009)

Thanks FinancialEngineer for showing the effects that payment timing can have on the calculation of return. When others were posting with very different answers from mine, I momentarily doubted my own finance and math training.


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## FinancialEngineer (May 28, 2013)

Robillard said:


> Thanks FinancialEngineer for showing the effects that payment timing can have on the calculation of return. When others were posting with very different answers from mine, I momentarily doubted my own finance and math training.


Talking of math, if you wanted to know how Excel is calculating the RATE then one of the following two calculations would be my guess

*TVM Eq. 1: PV(1+i)^N + PMT(1+i*type)[(1+i)^N -1]/i + FV = 0*

f(i) = 1240 + -100 * (1 + i * 1) [(1+i)^12 - 1)]/i + 0 * (1+i)^12

f'(i) = (-100 * ( 12 * i * (1 + i)^(11+1) - (1 + i)^12) + 1) / (i * i)) + 12 * 0 * (1+0.1)^11

i0 = 0.1
f(i1) = -1112.2712
f'(i1) = -16276.8568
i1 = 0.1 - -1112.2712/-16276.8568 = 0.0316654787075
Error Bound = 0.0316654787075 - 0.1 = 0.068335 > 0.000001

i1 = 0.0316654787075
f(i2) = -238.0733
f'(i2) = -9843.5869
i2 = 0.0316654787075 - -238.0733/-9843.5869 = 0.00747985742939
Error Bound = 0.00747985742939 - 0.0316654787075 = 0.024186 > 0.000001

i2 = 0.00747985742939
f(i3) = -19.9733
f'(i3) = -8240.0669
i3 = 0.00747985742939 - -19.9733/-8240.0669 = 0.00505592844508
Error Bound = 0.00505592844508 - 0.00747985742939 = 0.002424 > 0.000001

i3 = 0.00505592844508
f(i4) = -0.1767
f'(i4) = -8094.7493
i4 = 0.00505592844508 - -0.1767/-8094.7493 = 0.00503410537056
Error Bound = 0.00503410537056 - 0.00505592844508 = 2.2E-5 > 0.000001

i4 = 0.00503410537056
f(i5) = -0
f'(i5) = -8093.453
i5 = 0.00503410537056 - -0/-8093.453 = 0.00503410362274
Error Bound = 0.00503410362274 - 0.00503410537056 = 0 < 0.000001

*IRR = 0.503%*

--------------------------------------------------

*TVM Eq. 2: PV + PMT(1+i*type)[1-{(1+i)^-N}]/i + FV(1+i)^-N = 0*

f(i) = 0 + -100 * (1 + i * 1) [1 - (1+i)^-12)]/i + 1240 * (1+i)^-12

f'(i) = (--100 * (1+i)^(-12-1) * ((1+i)^12 + i * ((1+i)^12 -12-1) - 1)/(i*i)) + (1240 * -12 * (1+i)^(-12-1))

i0 = 0.1
f(i1) = -354.4039
f'(i1) = -972.4867
i1 = 0.1 - -354.4039/-972.4867 = -0.264430572619
Error Bound = -0.264430572619 - 0.1 = 0.364431 > 0.000001

i1 = -0.264430572619
f(i2) = 38614.7875
f'(i2) = -615967.6309
i2 = -0.264430572619 - 38614.7875/-615967.6309 = -0.201740935045
Error Bound = -0.201740935045 - -0.264430572619 = 0.06269 > 0.000001

i2 = -0.201740935045
f(i3) = 13007.5145
f'(i3) = -201379.7365
i3 = -0.201740935045 - 13007.5145/-201379.7365 = -0.137148962148
Error Bound = -0.137148962148 - -0.201740935045 = 0.064592 > 0.000001

i3 = -0.137148962148
f(i4) = 4216.0063
f'(i4) = -67618.0826
i4 = -0.137148962148 - 4216.0063/-67618.0826 = -0.0747986827129
Error Bound = -0.0747986827129 - -0.137148962148 = 0.06235 > 0.000001

i4 = -0.0747986827129
f(i5) = 1244.7462
f'(i5) = -24364.5504
i5 = -0.0747986827129 - 1244.7462/-24364.5504 = -0.0237102710388
Error Bound = -0.0237102710388 - -0.0747986827129 = 0.051088 > 0.000001

i5 = -0.0237102710388
f(i6) = 279.7758
f'(i6) = -10545.5769
i6 = -0.0237102710388 - 279.7758/-10545.5769 = 0.00281988140916
Error Bound = 0.00281988140916 - -0.0237102710388 = 0.02653 > 0.000001

i6 = 0.00281988140916
f(i7) = 17.1853
f'(i7) = -6747.2092
i7 = 0.00281988140916 - 17.1853/-6747.2092 = 0.00536689962363
Error Bound = 0.00536689962363 - 0.00281988140916 = 0.002547 > 0.000001

i7 = 0.00536689962363
f(i8) = -2.529
f'(i8) = -6458.985
i8 = 0.00536689962363 - -2.529/-6458.985 = 0.00497535329337
Error Bound = 0.00497535329337 - 0.00536689962363 = 0.000392 > 0.000001

i8 = 0.00497535329337
f(i9) = 0.4479
f'(i9) = -6502.5496
i9 = 0.00497535329337 - 0.4479/-6502.5496 = 0.00504423468596
Error Bound = 0.00504423468596 - 0.00497535329337 = 6.9E-5 > 0.000001

i9 = 0.00504423468596
f(i10) = -0.0772
f'(i10) = -6494.8663
i10 = 0.00504423468596 - -0.0772/-6494.8663 = 0.00503234931671
Error Bound = 0.00503234931671 - 0.00504423468596 = 1.2E-5 > 0.000001

i10 = 0.00503234931671
f(i11) = 0.0134
f'(i11) = -6496.1914
i11 = 0.00503234931671 - 0.0134/-6496.1914 = 0.00503440718274
Error Bound = 0.00503440718274 - 0.00503234931671 = 2.0E-6 > 0.000001

i11 = 0.00503440718274
f(i12) = -0.0023
f'(i12) = -6495.962
i12 = 0.00503440718274 - -0.0023/-6495.962 = 0.00503405108908
Error Bound = 0.00503405108908 - 0.00503440718274 = 0 < 0.000001

*IRR = 0.503%*


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## FinancialEngineer (May 28, 2013)

*I just wanna have fun, more fun in finding rates*

This isn't the end of the road, things would be more interesting had the OP deposited funds in account that grew each month by a growth rate

Say in first month, he deposited 100 but starting in the second month his deposits increased by 10% so the second deposit would be in amount of $110 and the third deposit would be in amount of $121 and so on till the last deposit in month 12 would be in amount of $285.31

Now the problem of finding the interest rate on this deposit is made complicated since we now also have to consider the inflation rate. Obviously the terminal value would now be more than the $1240 when the payments were in uniform series of $100

So how then you find this interest rate, Excel comes to mind but it offers no solution as the RATE function as I have told you earlier is based on one of the two TVM equations that are only valid when annuity payments are in constant amount

If you are avid Excel user then you would have to look at some of the offerings by 3rd party vendors that are not a household name and Microsoft is making every effort to copy and paste the ideas of other people to make a buck and deprive others of the hard work they have put in to make a product

The problem of including a gradient in the TVM equation has been implemented in an Excel add-in called tadXL that extends Excel's 5 TVM functions ( RATE, NPER, PMT, PV, & FV) and then introduces a new TVM function called GRADIENT

The gradient may be of two types, the one that I discussed in my example where annuity payments grows by a constant growth rate or shrinks by a shrink rate is called Geometric progression. The other type of progression is called Linear progression where annuity payments increase or decrease by a constant money amount.

Now you think what is possible with finding interest rates, inflation rates, number of periods, annuity payments, present value and future value for annuities that have a GRADIENT

And how about the option of using a value of infinity for NPER to find present value and interest rate on never ending payments.

I told you the fun never stops till the Feds drop the interest rates and the Japs and Chinese are happy that their investment in US Treasury notes are paying ever more dividends.

Someone said America used to be the largest CREDITOR nation  but since the time politically correct regimes took over Washington in the early 1990's things have gone 360 and now America stands to be the largest DEBTOR nation


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## MoneyGal (Apr 24, 2009)

Ooooh. Excel add-ins! http://www.qwema.ca/index.php/products-services/qvel/


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## FinancialEngineer (May 28, 2013)

MoneyGal said:


> Ooooh. Excel add-ins! http://www.qwema.ca/index.php/products-services/qvel/


4 people running a GROUP 

What they, QWeMA, have is applied stochastic calculus in financial analysis

I met people who told me of the future events, then they were proven wrong when what they predicted never occurred on the date they said it will occur

I call myself a Financial Engineer, that is a claim from someone with a high school equivalency diploma. A self taught financial analyst

And as far as I know, Yeshiva University in New York only offers studies in Judaism and not the more selfish subject of Money as claimed by the President, CEO & Chairman of QWeMA group


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## steve41 (Apr 18, 2009)

There is a point where elaborate equations simply don't do the job..... you need to resort to recursive math. Very inelegant, but infinitely more flexible, especially in the current personal computer environment.


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## FinancialEngineer (May 28, 2013)

*And I thought I could read people's faces*



steve41 said:


> There is a point where elaborate equations simply don't do the job..... you need to resort to recursive math. Very inelegant, but infinitely more flexible, especially in the current personal computer environment.


Hey you! Are you a mind reader or can you see through other people's program code?

This I say as the 6 TVM functions in tadXL do not use an "Equation" to solve for GRADIENT, RATE, NPER, PMT, PV & FV. 

*Recursion* you said, mine solution is *iterative* but still gets the results


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## FinancialEngineer (May 28, 2013)

steve41 said:


> There is a point where elaborate equations simply don't do the job..... you need to resort to recursive math. Very inelegant, but infinitely more flexible, especially in the current personal computer environment.


This German guy http://www.office-loesung.de/ftopic311173_0_0_asc.php#2516944 I communicated with to get help with localization asked whether tadXL was using behind the scenes annuity tables to find present value of growing annuities where growth did not coincide with annuity payments and if add-in file size was in mega bytes to which I replied file size is 388 KB and there weren't any tables.

He stopped talking to me ... So now I am left with a tadXL Deutsch without any way of writing the help pages


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## Toronto.gal (Jan 8, 2010)

FinancialEngineer said:


> And as far as I know, Yeshiva University in New York only offers studies in Judaism...........


No, it's not just for rabbinic studies.
http://www.yu.edu/academics/


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## FinancialEngineer (May 28, 2013)

*I didn't know there was such a thing as a Secular Jew*



Toronto.gal said:


> No, it's not just for rabbinic studies.
> http://www.yu.edu/academics/


Yes I now read from that page that curriculum includes more than religious centric courses

Would I qualify for admission though?

Here is a list of my particulars:

1) I eat Kosher or something that resembles Kosher
2) I am circumcised
3) I have a son named Abraham
4) Lived in NY for about 7 years
5) I lay claim to half of Jerusalem, which half it is please do not ask
6) Hebron is where my son will be buried


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## FinancialEngineer (May 28, 2013)

You know I have been through many forums and understand that all the fun can be taken away by the owners of the forum

Take Google for example, which is nothing more than Bengali magic and computer software intertwined in one place. Google forums are of the view that anyone who happened to come across their site is their honored slave who gets trapped in a dungeon that they have built from which there is no escape for those who have potential to make Google money

This is the world we live in where people who do not qualify for a job at City Hall in Chicago happen to hold Highest Office of the Land

** 
_This is a family friendly website, please read rules of the forum._


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## peterk (May 16, 2010)

I like this crazy new guy. :encouragement:


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## Toronto.gal (Jan 8, 2010)

FinancialEngineer said:


> Yes I now read from that page that curriculum includes more than religious centric courses


Given what the QWeMA Group Inc. is about, why would you have thought that Dr. Moshe Milevsky had just studied religion at the Yeshiva University?
http://en.wikipedia.org/wiki/Moshe_Milevsky


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## FinancialEngineer (May 28, 2013)

Toronto.gal said:


> Given what the QWeMA Group Inc. is about, why would you have thought that Dr. Moshe Milevsky had just studied religion at the Yeshiva University?
> http://en.wikipedia.org/wiki/Moshe_Milevsky


I thought someone from New York wanting to study business will find New York University's Stern Business school as a prime destination rather than Yeshiva. 

But then one may be short of cash as NYU's business program costs an arm and a leg in comparison Yeshiva's annual tuition fee in the year 1986 was $300. 

But then I didn't even have the $2 bus fare in 1986 from Yonkers to New York City so for me even Yeshiva was an expensive place to study.


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## FinancialEngineer (May 28, 2013)

Toronto.gal said:


> http://en.wikipedia.org/wiki/Moshe_Milevsky


Oh I remember Wiki, the darling, the mistress, the girlfriend of Almighty Google. Ofcourse Wiki deserves to be Numero Uno on Google SERPS who would doubt the credibility and authenticity of the material on Wiki.

Only if Jimmy Wales distributed part of his annual donations of $20 million to those who have written the pages that is Wiki.

But just as I know, you will never win an argument with Google or may I say those at Google don't like to lose an argument.

If you have ads on your site, it will get penalized for being taken as SPAM.

But then when I took all ads off my site(s) I lost my SERPS to those sites that have Google Adsense.

The conclusive evidence would suggest that if Google is not making money from you then those whose sites are making Google money will be rewarded up the ranks.

This is kinda like the US Department of Justice approach of punishment and reward. Those who make DOJ money by running nation wide criminal networks get to wine and dine with the Justices that are suppose to be fighting the same crooks. And those who are the street peddlers of crack "cocaine in crystal form" are given 10 years at the least at State prisons.


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## lonewolf (Jun 12, 2012)

Someone said America used to be the largest CREDITOR nation  but since the time politically correct regimes took over Washington in the early 1990's things have gone 360 and now America stands to be the largest DEBTOR nation [/QUOTE]

Hi, financialengineer

Welcome to the forum

Being the largest debtor nation will make the American dollar strong. Trade the world for the American dollar cycle is coming.


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## FinancialEngineer (May 28, 2013)

lonewolf said:


> Hi, financialengineer
> 
> Welcome to the forum
> 
> Being the largest debtor nation will make the American dollar strong. Trade the world for the American dollar cycle is coming.


Staying on the same footing, I recall receiving an email from a international sales manager at a major software reseller [VAR]. He stated in his email that he has a client who is interested in purchasing 100,000 licensed copies of tadXL which at the time was available as version 1 priced at US$39. The latest version 2.0 costs $99 per license.

In closing of his email he said *he was short on time and asked me to contact him in a hurry if I wanted the sales.*

Now here is what I said to him in my reply.

" *tadXL is only available for sales and distribution in selected countries* including the following:

1) US, and Canada (North America)
2) UK, countries in Northern, and Western Europe plus Italy, Spain and Portugal
3) Australia and New Zealand
4) Israel

I explained to him that *other countries in Middle East* have an option to give away their *Petro Dollars* to *Halliburton* in *exchange for security*.

And that those countries in *Far East* including *China, South Korea and Japan* may want to *reinvest* their *Interest payments from the US Treasury Bills elsewhere*

As *I didn't need any body else money*."

*I never heard back from the sales manager.* 

So was that a *sane decision* on my part to *let go off income* in amount of *$3,900,000* that would have made me an *instant millionaire*.


Thinking of it, *the answer is yes*. At least I *didn't sell out* to *foreign interests unlike the politicians* in *Washington D.C*., Ottawa, or other capitals of the Western World.

My *web enterprises* may be on a course of *economic hardships* but I manage to stay afloat with a *4 or 5 sales a month* earning me *$500*


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## Toronto.gal (Jan 8, 2010)

FinancialEngineer said:


> Yeshiva's annual tuition fee in the year 1986 was $300.


Even for 1986, that fee seems low. Today's value would be $630.19. I used a calculator for this, not a formula. 

Currently, the tuition fee = $47,074 for all expenses/$188,296 for a 4 year BA [$145,696 without room & board].

As for why anyone would attend YU over other universities, surely you know it's the dual curriculum.


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## Ponderling (Mar 1, 2013)

FinancialEngineer said:


> Talking of math, if you wanted to know how Excel is calculating the RATE then one of the following two calculations would be my guess
> 
> TVM Eq. 1: PV(1+i)^N + PMT(1+i*type)[(1+i)^N -1]/i + FV = 0[/B]
> 
> ...


All of this takes me back to my Engineering Economics course, so many years ago. I still have the text, tabbed where I reference it more that once. 

Yes, some of the IRR's and the like had/have to be solved iteratively to get the error down; the formulation for some calulations is too tortured to isolate the desired variable on it's own.

I still use the book, but not did at first dare speak of regualrly pulling out a now over 25 year old Uni text as a reference in this digital age.


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## FinancialEngineer (May 28, 2013)

Toronto.gal said:


> As for why anyone would attend YU over other universities, surely you know it's the *dual* curriculum.


Some in New York State resent the Jewish community for having *dual* citizenship


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## FinancialEngineer (May 28, 2013)

Ponderling said:


> J


Please! I hope that letter J at the bottom of your Quotation was a typo

As I have horrible memories of my encounter with a New York City DJ who went by the media name of Jay Diamond

I guess Jay's love for his people was more than his love for his country.


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## CanadianCapitalist (Mar 31, 2009)

FinancialEngineer said:


> I guess Jay's love for his people was more than his love for his country.


That was a square bracket, probably a typo from deleting the full quote. Stop being so paranoid.


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## FinancialEngineer (May 28, 2013)

CanadianCapitalist said:


> That was a square bracket, probably a typo from deleting the full quote. Stop being so paranoid.




I only realized that after I had made the post, guess it was too late to delete the post


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