Algorithms

Dan Neely10-Oct-07 7:16

Dan Neely

10-Oct-07 7:16

There's been exactly *one* actual study on this sort of lending. With the cooperation of a South African bank they took a group of people who were just under the approval threshold for a loans with average values of ~1000, and 4 monthly payments of ~360 (don't recall if values were in US or local currencies) and granted approval to half of them anyway. They then did a 6mo followup on both groups and found the ones that had been granted the loan were on average better off financially than those that had been denied. I read about it in a recent issue of The Economist, but since I don't save back issues I can't tell you which one it was.

--
If you view money as inherently evil, I view it as my duty to assist in making you more virtuous.

DQNOK10-Oct-07 6:31

DQNOK

10-Oct-07 6:31

see http://www.public.asu.edu/~subhro/pup622/localfinance/sld008.htm[^] but substitute the MONTHLY RATE for 'r' in the formula if you are using 'n' as the number of months.

Assuming you actually meant 23.99 APR, (which equates to ~ 2% per month) the formula gives: $236.40. I built a quick spreadsheet to verify that this payment amount will in-fact pay off the debt in 12 months, and it does. This payment number is slightly different than your number, so I'm wondering if your interest is being compounded differently.

David

Vtoria10-Oct-07 6:34

Vtoria

10-Oct-07 6:34

Can you forward me that spreadsheet? Is it in Excel?
The APR is in fact 239.9961%.

Victoria

DQNOK10-Oct-07 7:04

DQNOK

10-Oct-07 7:04

See your e-mail account you posted with CodeProject. I don't know how to post files.

David

Vtoria10-Oct-07 7:11

Vtoria

10-Oct-07 7:11

I don't have anything. But you can send it to vtoriagarcia@aol.com

Thank you!

Victoria

Paul Conrad12-Oct-07 17:04

12-Oct-07 17:04

Vtoria wrote:
The APR is in fact 239.9961%

Sorry, but that is just insane...

Only an idiot would go with that.

"Find it your bloody self - immediately!" - Dave Kreskowiak

Vtoria10-Oct-07 6:41

Vtoria

10-Oct-07 6:41

The interest is accrued daily on the principle balance; just like a mortgage.

Victoria

Homework Question - honest!!

Jerry Jeremiah15-Oct-07 10:57

Jerry Jeremiah

15-Oct-07 10:57

Take a look at this article from the FAQ of Dr. Math:
http://www.mathforum.org/dr.math/faq/faq.interest.html[^]

In an installment loan, a lender loans a borrower a principal amount P, on which the borrower will pay a yearly interest rate of i (as a fraction, e.g. a rate of 6% would correspond to i=0.06) for n years. The borrower pays a fixed amount M to the lender q times per year. At the end of the n years, the last payment by the borrower pays off the loan.

The amount of the fixed payment is determined by:

M = P * i / [ q (1 - [1+( i / q)]^(-n* q) ) ]
M = 2500 * 2.399961 / [26 (1 - [1+(2.399961/26)]^(-1*26) ) ]
674653127756771870877187207 (which, when rounded to 2 dp is $256.61)

The total amount paid by the borrower is Mnq, and the total amount of interest paid is I = Mnq - P:

I = M * n * q - P
I = 256.60 * 1 * 26 - 2500
I = 4171.7754098132167606864280686738 (which, when rounded is $4171.78)

That is a lot of interest!

Jerry
http://www.mathforum.org/dr.math[^]

Malcolm Smart6-Oct-07 5:34

6-Oct-07 5:34

My lad has just come home with this....

A lemming runs towards a cliff at 4m/s. He jumps of and falls at 25 m/s. Assume vertical drop, not inertia, etc. The whole distance travelled is 500m. The time taken = 41seconds. How tall is the cliff?

4m/s
A-------------B
|
|
| 25m/s
|
|
C

A to C = 500 meters. Time Taken = 41 seconds. We know the answer is 400 meters, but no idea how to get there. I've worked on S = D/T

41 = 4 + 25
----- --
500-x x

Any ideas? He won't just submit the answer - he will understand it - honestly!!

Cheers

Malc 'frustrated' Smart

"More functions should disregard input values and just return 12. It would make life easier." - comment posted on WTF

"This time yesterday, I still had 24 hours to meet the deadline I've just missed today."

Luc Pattyn6-Oct-07 6:16

6-Oct-07 6:16

Malcolm Smart wrote:
41 = 4 + 25
----- --
500-x x

Not sure how to read this, it does not appear in my approach though:

say x = horizontal distance to reach cliff
say y = height of cliff

then total distance = x+y = 500 m

and total time = horizontal time + vertical time = 41 sec

so write down these times as an expression in x and y, you get a system of two
linear equations with two variables, that easily gets solved.

And indeed x=100, y=400 m

BTW: real lemmings would follow a parabola, with an increasing vertical speed due to
gravity, until air friction would stop the vertical acceleration...

Smile | :)

Luc Pattyn [Forum Guidelines] [My Articles]

this months tips:
- use PRE tags to preserve formatting when showing multi-line code snippets
- before you ask a question here, search CodeProject, then Google

Malcolm Smart6-Oct-07 7:08

6-Oct-07 7:08

Thanks Luc

Can you go that one step further with the two linear equations (or at least one of them..?)

He's not submitting the homework as we've admitted defeat, so he isn't cheating - I wouldn't let him. Honest!! And it's now more for me than him.

We've got distance = speed / time.

and from that

distance x = 4ms / ?
distance y = 25ms / ?

but now stumped.

Cheers

Malc

....and if I ever saw a real lemming after swatting through this, it wouldn't follow a parabola - I'd stamp on it.

Luc Pattyn6-Oct-07 7:33

6-Oct-07 7:33

Malcolm Smart wrote:
We've got distance = speed / time

that's a new kind of physics to me: the shorter you travel the farther you go?

as one of my professors repeated over and over: check the dimensions (units must match
on both sides).

Smile | :)

Luc Pattyn [Forum Guidelines] [My Articles]

this months tips:
- use PRE tags to preserve formatting when showing multi-line code snippets
- before you ask a question here, search CodeProject, then Google

Malcolm Smart6-Oct-07 9:00

6-Oct-07 9:00

OK - we've now got (after punching him repeatedly for using a made up formula....)

x = unknown time

total distance = (speed*time falling) + (speed*time running)
500 = 25x + 4(41-x) //41 - total time, x = time spent falling
500 = 25x + 164 - 4x
336 = 21x
x = 16.

25 * 16 = 400 - cool!!!

Thanks for not giving the answer - made us both think, and to realise something fundamental was wrong - distance = speed * time - doh.

I'll stick to C#, Higher Grade GCSE isn't my thing... Blush | :O

)

Luc Pattyn6-Oct-07 9:42

6-Oct-07 9:42

Malcolm Smart wrote:
Thanks for not giving the answer

You're welcome, always happy to help ... a little. Big Grin | :-D

Malcolm Smart wrote:
I'd stamp on it.

Malcolm Smart wrote:
after punching him repeatedly

Please keep violence against kids and animals down to the necessary levels. Mad | :mad:

Luc Pattyn [Forum Guidelines] [My Articles]

this months tips:
- use PRE tags to preserve formatting when showing multi-line code snippets
- before you ask a question here, search CodeProject, then Google

Paul Conrad6-Oct-07 9:46

6-Oct-07 9:46

Luc Pattyn wrote:
say x = horizontal distance to reach cliff
say y = height of cliff

then total distance = x+y = 500 m

and total time = horizontal time + vertical time = 41 sec

so write down these times as an expression in x and y, you get a system of two
linear equations with two variables, that easily gets solved.

And indeed x=100, y=400 m

Hmmm, I have an Algebra test to administer next week, and I might just throw this at my students :->

"Find it your bloody self - immediately!" - Dave Kreskowiak

Dan Neely8-Oct-07 2:12

Dan Neely

8-Oct-07 2:12

Luc Pattyn wrote:
BTW: real lemmings would follow a parabola, with an increasing vertical speed due to
gravity, until air friction would stop the vertical acceleration...

For something as small as a lemming terminal velocity would be reached very quickly so a constant linear velocity isn't a bad approximation.

--
If you view money as inherently evil, I view it as my duty to assist in making you more virtuous.

Luc Pattyn8-Oct-07 2:21

8-Oct-07 2:21

That would depend on the fur condition, hence the season.
Anyway, initially it would not be 25m/s so the real cliff would not be as tall.

Smile | :)

Luc Pattyn [Forum Guidelines] [My Articles]

this months tips:
- use PRE tags to preserve formatting when showing multi-line code snippets
- before you ask a question here, search CodeProject, then Google

Dan Neely8-Oct-07 3:08

Dan Neely

8-Oct-07 3:08

Luc Pattyn wrote:
That would depend on the fur condition, hence the season.

Not much, even hairless they'd have a very low terminal velocity due to their low mass. The exact value might change slightly but that it would be very slow would remain a constant.

Luc Pattyn wrote:
Anyway, initially it would not be 25m/s so the real cliff would not be as tall.

True, but with an initial acceleration of 9.8m/s/s, and the drag resulting in something similar (in appearance at least) to an exponential approach terminal velocity would be reached in 3ish seconds, with >90% of the fall near terminal velocity the initial conditions will have a fairly small impact on the result.

--
If you view money as inherently evil, I view it as my duty to assist in making you more virtuous.

Paul Conrad6-Oct-07 9:32

6-Oct-07 9:32

Malcolm Smart wrote:
The whole distance travelled is 500m. The time taken = 41seconds. How tall is the cliff?

Pretty damn tall :->

"Find it your bloody self - immediately!" - Dave Kreskowiak

Malcolm Smart6-Oct-07 9:39

6-Oct-07 9:39

and it won't be just lemmings going over it if he ever gives me the wrong formula to work with again...... (perhaps I should have known better... D'Oh! | :doh:

)

Luc Pattyn6-Oct-07 9:45

6-Oct-07 9:45

First rule of debugging: don't trust anything or anyone.

Smile | :)

Luc Pattyn [Forum Guidelines] [My Articles]

this months tips:
- use PRE tags to preserve formatting when showing multi-line code snippets
- before you ask a question here, search CodeProject, then Google

Paul Conrad6-Oct-07 9:47

6-Oct-07 9:47

Luc Pattyn wrote:
First rule of debugging: don't trust anything or anyone

Good point Big Grin | :-D

"Find it your bloody self - immediately!" - Dave Kreskowiak