OKay smart guys, try your hands on this one [Math problem]

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A real world Math problem at that! First I'll provide the long version / background situation just so you're not boxed in with your responses, and then we'll see if we can't solve the specific problem I'm running into for the method I've chosen. Here goes:

I have four loan accounts I'm trying to pay off. They each have their own interests, including one with a promotional interest that'll end in a year. I have dedicated a certain amount to paying these off every month, so that all four payments must add up to this amount monthly.

How do I determine the minimum interest payments (grand total, across all four accounts throughout the lifetime of all the loans), and the payment schedule that'll yield this minimum?

No, it will not be achieved by only paying off the highest interest account at once. Something about the second highest just sitting around unpaid, and also the promotional account which will then burst in my face after the one year interest-free period.

What do you think?

So far, I've used Excel and MATLAB. They're helpful, but recently I realized that they're just that: software programs. They're not smart, because even though I can use them to minimize monthly interest, they don't know that the last account will blow up in 12 months and the interests will sky-rocket again. They can simply only do what I tell them, and so far I'm not telling them all they need to know; I just don't know how.

My idea now (after the 17 or 18 that I threw out), is to generate four matrices, the corresponding contents of which each add up to the total dedicated payment (let's call it $600). Each of those matrices can and should have values that range from 0 to 600, with a specified density, maybe 0.5 or .25 for each step. When I get these four matrices, I'll plug each set of four into each step (month) for the payments, and then plot a graph showing me the total interest, and then visually choose which payment scheme is the cheapest.

Another area I was looking into was a MATLAB function, it locates a minimum value, but based only on a function. I don't have a function. I have a multitude of "if else" statements and iterative equations. Still, I think it just might work and I'd like to give it a try. But alas, I don't have the toolbox (Optimization toolbox). If anyone has it, let's chat :hi:

Other than that, any other ideas, feel free to gimme a shout out! Thanks!!

PS: Those of you high school students wondering what you'll ever use Math for, consider this a prime example. If I solve this problem, I get to pay up the least amount of money (not considering better consolidation and additional balance transfers, of course). Else, I'm stuck wasting money I really shouldn't have. :thumbs: Wish me luck!

posted by  JaneiR36

SHUT UP! :banghead:

posted by  Ki2AY

lol I bet I lost you at the first sentence, you fking dumbass :laughing: Like, for real! Not even an Internet insult, a real life dumbass who cannot comprehend a real life problem. Truly sad.

posted by  JaneiR36

I must admit, you lost be but my excuse will be that i'm still in highschool so i havent learned TOO much of what your talking about yet. Thats my excuse and i'm sticking to it :mrgreen: . But i will wish you luck and hope you find out what you need to know in order to get the better deal. Good luck with finding what you need and what is better for you. :thumbs:

posted by  car_crazy89

I'm on it, Janei!!!

(*starts calling up jewish friends*)
I've printing it out now. I'll give it a shot in my next class (ironically, which is math). I'll get at least one answer by the time I get home

posted by  Godlaus

ehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh shut up! YOU TALK TO MUCH.

posted by  Ki2AY

You're the best!!! :thumbs:

I got so tired of working on that crap, I decided to just throw it into cyberspace and hopefully someone would have something by the end of the day. Wish I had posted actually numbers so you all could test it out, though. But I'm pretty sure you should be able to come up with something.

Thanks again!! If nothing, for the interest...lol.

posted by  JaneiR36

That must be your way of saying you miss me seeing as I haven't been posting much at all recently.

posted by  JaneiR36

K, the problem completely defeated me in math class, mostly because I had a total of 10 minutes to work on it, but, I'll give it another shot when I get home (In about 4 hours), I'll get back to you later.

posted by  Godlaus

Ugh...I dunno what there is to do, I can't find any loopholes in it.
(Presuming stuff here)
There are 4 loans,

Loan A (10%)
Loan B (7%)
Loan C (6%)
Loan D (20% at the end of the year)

Therefore, with the money you make, you should pay the interest (minimum possible) on loans A,B,C, and give as much as possible to get rid of D.

Of course, this is too simple of an answer, so, what am I missing? Are these loans not locked in rates? Are the exponetionally raising? What am I not taking into effect?

posted by  Godlaus

A) you have freaking great rates
B) whats the minimum monthly payments
C) whats the loan amounts(if you dont mind!)
D) how much can you pay per month?
E) are those the yearly interest rates?

b+c+d will definitely help solve the equation

obviously youll be paying less monthly on the first 3, and more on the fourth.

for example, you have 600$ per month to spend on these loans

lets take it simple for the first go, and go with next years interest, all loans for 1k flat, and assume that those are yearly interests.

1000x(interest, in decimal value)/12
Loan A (10%) - approx monthly interest = 8$
Loan B (7%) - approx monthly interest = 6$
Loan C (6%) - approx monthly interest = 5$
Loan D (20%) - approx monthly interest = 16$

now lets say, the minimum monthly has to be interest + 20$

A) 28.00$
B) 26.00$
C) 25.00$
D) 36.00$

right there, is 115$ per month
that leaves you with what, 485$ to spend on loans.

now this is the fun part, figuring out how much each one gets.
lets assign a percentage value to each one, according to their interest rate.
the 43 comes from total interest per month(20+10+7+6)

A) 10/43x100 = 23.25%
B) 7/43x100 = 16.25%
C) 6/43x100 = 14%
D) 20/43x100 = 46.5%

now lets give those percentages a monetary value.

485x(percentage, in decimal value)
A) 23.25% = 112.76$
B) 16.25% = 78.81$
C) 14.00% = 67.90$
D) 46.50% = 225.53$

so for the first month, you would have payment amounts of
A) 28.00 + 112.76 = $140.76
B) 26.00 + 78.81 = $104.81
C) 25.00 + 67.90 = $92.90
D) 36.00 + 225.53 = $261.53

forgive me if i screwed up, but that seems to add up to 600$...

so for month two!

Loan A's value is now 859.24$
Loan B's value is now 895.19$
Loan C's value is now 907.01$
Loan D's value is now 738.47$

interest this month: A)7$ B) 5$ C) 4$ D) 12$
minimum payments: A) 27$ B) 25$ C) 24$ D) 32$
percentages remain steady
amount you can sink into each loan(108$ into minimums, 492$ left over)
A) 114.39$ B) 79.95$ C) 68.88$ D) 228.78$

total payment amounts:
A) 141.39$ B) 104.95$ C) 92.88$ D) 260.78$

values after two months:
A) 717.85 B) 790.24 C) 814.13 D) 477.69

interest: a) 6$ b) 4$ c) 3$ d) 8$
mins: a) 26 b) 24 c) 23 d) 28
percentages steady
amount into each loan (101 into mins, 499$ left)
a) 116.02 b) 81.09 c) 69.86 d) 232.03
total amount:
a) 142.02 b) 105.09 c) 92.68 d) 260.03

after three months
a) 575.83 b) 685.15 c) 721.45 d) 217.66

Month Four
interest: a) 5 b) 4 c) 3 d) 4
mins: a) 25 b) 24 c) 23 d) 24
Well, now a different loan is on top, so the percentages must be adjusted to compensate. lets take half of the difference between D an A, and give it to A.
new percentages: a) 35.25% b) 16.25% c) 14.00% d) 34.50%
amount into loans (96 mins, 504 left over)
a) 177.66 b) 81.90 c) 70.56 d) 173.88
totals into loans
a) 202.66 b) 105.90 c) 93.56 d) 197.88

after four months:
a) 373.17 b) 579.25 c) 627.89 d) 19.78

this month, we will remove loan D, because it will make it easier to calculate
interest: a) 3$ b) 3$ c) 3$ d) none
mins: a) 23 b) 23 c) 23 d) 20$ to clear. (total: 89, left: 511)
percentages, redone...
A)10/23 = 43.5 B)7/23 = 30.5 C)6/23 = 26.0
amount into loans:
a) 222.29 b) 155.86 c) 132.86
total into loans:
a) 245.29 b) 178.86 c) 155.86 d) 20.00

after five months
a) 127.88 b) 400.39 c) 472.03

month six - second debt is done!
this month, we will remove loan A.
interest: a) 1$ b) 2$ c) 2$
minimums: a) 129$ b) 22$ c) 22$ (total: 173, left: 427)
percents = 50%
into loans: b) 213.5 c) 213.5
total into loans: a) 129 b) 235.50 c) 235.50

after six months:
b) 164.89 c) 236.53

month seven, your done!
interest: b) 1 c) 1
payments: b) 166 c) 238


according to those calculations...
interest per month:
1: 35
2: 28
3: 21
4: 16
5: 9
6: 5
7: 2

total interest paid out: 116.00$

well, that wasted a solid 30 minutes....now what else can i do for the rest of the night?...

posted by  dodgerforlife

http://www.richmore.com/mortgage/excel/ :doh:

posted by  lectroid

Haha that might help and be alittle more accurate and easier to use. To bad you didnt have that BEFORE dodgerforlife wasted more then enough of his time on that lol. :mrgreen:

posted by  car_crazy89

:laughing: Why beat yourself up? When someone else can beat themself up for you. :screwy:

posted by  lectroid

Haha true enough. You make a good point :thumbs: lol.

posted by  car_crazy89

Dayum :doh:

posted by  SubaruCorsi

considering i only used THIRTY of my PRECIOUS minutes, it isnt too bad at all.

And considering most people dont use Excel, what the hell good does it do to just send them a link on how to create a spread for it?

posted by  dodgerforlife

The link shows you how to calculate the payment schedule for a whopping one loan. It also assumes a fixed lifetime of the loan. Awesome if you're calculating your mortgage or student loan schedule, payments that have a low interest rate and a longer lifetime, for which you won't necessarily benefit that much from paying quickly.

For example, I have a student loan acct that's in repayment. I've calculated that if I pay 88% more than my minimum payment, or per month, I'll be able to pay my entire interest back tax free (it's an incentive for paying back loans quickly, I guess. They allow up to $2500 tax-free, or something like that). But after calculating how much I saved, on a 2 or 3% interest loan, with savings over a 10 or 20 year lifetime of the loan, I'd rather keep that money in my pocket than go broke trying to speed-pay a long-term, low-interest account. In this case, or in the case of a mortgage, the original payment schedule would typically be the way to go. For me, anyway.

But we're talking about juggling four accounts here to pay the minimum over the lifetime of all loans put together. It's a whole different ballgame.

Are you sure? :wink2: It's interesting how your calculations simply came up with what common sense (and financial advisors) tells us. Good job! :thumbs: That's what I've been told, too. However,...

Let's put some numbers to this:

Loan A: $2800 @ 9%
Loan B: $3000 @ 15%
Loan C: $2500 @ 19%
Loan D: 4000 @ 10%, initially 0% for 12 months.

Now using the common sense approach, while you're funneling all the money to, say a $500 balance left on the Loan C account, you're having 15% of interest getting charged to an unscathed, say, $2800 left on the Loan B account. 15% is not 19%, but the actual interests amounts say something that should be taken into consideration in calculations.

The second problem I see, is that the Loan D account gets ignored by the common sense approach for 12 months. And then at the 12 month mark, the whole thing balloons in your face. The full 10% is charged, also on the barely scratched surface of the initial loan amount.

It's entirely possible that even after total optimization, the change in total interest charged is not that much. I'm just curious as to what the amount is, and whether or not it'll make a difference.

Which is why from Excel, I'm moving into a stronger Math program like MATLAB. It can calculate the total interest for any number of payment schedules (the speed of my processor permitting), and plot a graph, from which I can locate the schedule that costs the least interest. I'm just having trouble coming up with the schedules.

dodgerforlife, now you have b c & d as requested. One note on your calculations...

My problem with this step is you're allocuting money to the loans based on interest rates. So if I have $10 left on loan D and $3000 left on loan C, does that still hold? Other than that, good job! I can see the steps you've taken in your calculations and most of them make sense.

Did anyone look into the matrix I mentioned?

A four rowed matrix, the columns of which each add up to 600. And the entire range of 0 to 600 is represented in each of the rows. I was about to do an example that was simply a 4 x 7 matrix, but even that got too hard. Surely there's a program that does this!! But which one?!?! :banghead:

(I'll have to research some Math forums on the weekend, but for now, I'm bugging you guys :laughing: )

posted by  JaneiR36

Perhaps your putting too much effort into this. How is your credit rating? Do you often get credit card offers for promotional rates? If the answer is yes then your answer is easy. You play the shell game.

You throw the majority of your money at the higher interest card until you can transfer its balance according to a promotional rate and perhaps even consolodate some of the other balances. The goal is to get everything consolodated to one card at a promotional rate. Then when that rate gets close to running out, you find another.

You may be amazed at how these credit cards will compete for your business.

This can have the effect of helping your credit rating as long as you make your payments. Another tip is to cancel out cards that you no longer use.

I have been doing this for years and have just done it recently. I had to buy a car for my wife to use on her longer commute. Didn't want to finance since were still paying for the last car we bought. So I put it on one of my cards with a 3.9% promotional offer and I applied for another card that has a 0% promotional offer until the balance is paid in full. Yes, paid in full. So if all works out I will have financed that car for 0% until I pay it off. Of course I will be making minimum payments on that card.

So, long winded answer but if you can play the shell game then that is the way to go.

posted by  theman352001

Janei, like I said, it was using simple numbers, the formulas could be modified for the amounts noted, you would simply weight the loans based on the amount/interest.

lets think about this for a moment. Because you only get that promotional rate for 12 months on loan d, and then it ballons, lets assign it half interest values, so that you start grinding it down.

Loan A: $2800 @ 9%
Loan B: $3000 @ 15%
Loan C: $2500 @ 19%
Loan D: $4000 @ 5%

(loan amount/total amount of loans)
percentage of total loans out
a = 23.00%
b = 24.00%
c = 20.00%
d = 33.00%

(interest rate/total interest)
percentage of interest total per month
a = 18.75%
b = 31.25%
c = 39.50%
d = 10.00%

now all that would need to happen is to figure out how to weight each payment according to their percentage of interest against the percentage of the loan value. obviously it will mean that the 10.00% you see for loan d would slide upwards a bit, to try and compensate for the size of the loan, just like the amount of 39.50% for c would slide down, also to compensate for the size(or lack thereof) of the loan.

and that, is where i lose. i sucked in math at high school lol.

lets see what someone else whos better at math can do with that.

EDIT: Oh yeah, if you noticed, I started to play with the percentages of the amount you put onto each loan according to the amount of interest you would be paying per month...

posted by  dodgerforlife

Exactly. You can play with the percentages (even though I still disagree that percentage interest is the way to go), but what is the optimal percentage distribution that'll give the lowest interest?

theman...... yeah, I already mentioned that. All the calculations will be done before and pending any 0% finance offers or balance transfers. There's even additional tweaking to be done, where after the 0% cards are paid every month, the excess is still transferred to the higher APR cards.

The initial calculations will give the best worst scenario.

Where no lower APR's are guaranteed, or the only credit limit offered doesn't cover the entire amount. (As things are looking like they might be).

I also happen to be curious about the Math problem, itself!

posted by  JaneiR36

do you have pictures in dr's post your pic thread? id like to see you, maybe just maybe you might be a hot mama afterall.

posted by  Ki2AY

I was up for a challenge but not one that required that much reading.

posted by  boothe

Communication skills are key. You can't understand or solve a problem if you don't take the time to read or listen. You may have been up for a challenge, but I very much doubt you'd have been able to solve it. Probably would have wound up coming back with a half baked solution 'cos you missed some points of the problem statement. :2cents:

posted by  JaneiR36

I'm not.


posted by  JaneiR36

are you sure about that?

tip 1: how to know if a women is hot over the internet :mrgreen: :

solution:women who denies their beauty. :orglaugh:

posted by  Ki2AY

Sorry, I'm not following you on this.

I'm suggesting that you move balances yourself based on the offers you receive. For example, when the 0% is about to run out on the $4000 loan, you should get another 0% offer that you can apply for, pay off the $4000 loan, and still have 0% for another period of time. If that $4000 was on a credit card, cancel the card to keep your total outstanding credit lower.

This actually has the effect of making that credit card want your business back and they may counter with another offer which you could use to transfer one of your other cards and perhaps get that to 0% also.

When you can do that, the problem is easy. You pay off your highest % cards first.

Obiously, it can be done. I would love to help out but it just doesn't interest me that much. My suggestion would be to break the problem into 2 parts: pre-0% offer expiration and post-0% offer expiration. Look at your condition after the offer expiration and that may help you decide the best course of action before the expiration.

Good luck.

posted by  theman352001

Yes... I just wish it was a smaller problem, thats all I meant. like:


ps. don't try that one.

posted by  boothe

Don't worry about it, then.

nah... MathCAD would knock that one out in two seconds. You'd use something called a "Given... Solve" statement. I liked that one a lot.

posted by  JaneiR36

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