Anyone know the mathematics for this (1 Viewer)

[Mike375]

I have the following done in Access but it is doing it by running "backwards" and "forwards" so to speak. Is the maths required Calculus?

We have two types of insurance policy (it could be two of any product type)....

1) Policy pays a benefit on death, disability but has no savings element. The premium for a given amount of benefit is $100

2) Policy pays a benefit on death, disability but has a savings element. Thus the premium for the same benefit as Policy 1 is $500

If the person has $500 then they can get the insurance benefit required with Number 2 policy. If they only have $100 then they can only buy Number 1 policy.

If they have $300 (or any amount between $100 and $500) what will the split between Policy 1 and Policy 2.

In other words if the benefit required is $100,000 how much of the benefit will be via Policy 1 and how much via Policy 2 while fitting a $300 premium.

 

[Dru995]

hmm.. looks like a linear programming problem to me.

 

[Darth Vodka]

I have the following done in Access but it is doing it by running "backwards" and "forwards" so to speak. Is the maths required Calculus?

We have two types of insurance policy (it could be two of any product type)....

1) Policy pays a benefit on death, disability but has no savings element. The premium for a given amount of benefit is $100

2) Policy pays a benefit on death, disability but has a savings element. Thus the premium for the same benefit as Policy 1 is $500

If the person has $500 then they can get the insurance benefit required with Number 2 policy. If they only have $100 then they can only buy Number 1 policy.

If they have $300 (or any amount between $100 and $500) what will the split between Policy 1 and Policy 2.

In other words if the benefit required is $100,000 how much of the benefit will be via Policy 1 and how much via Policy 2 while fitting a $300 premium.

sounds like compound interest to me...

not quite sure i get it though... for policy 1) you pay a premium of $100, what is the benefit paid out?

and for 2) what is the savings part? how is the benefit calculated?

 

[Dru995]

Assuming you want to pay as much as possible to policy 2 (to get the savings aspect) how I'd spend the £300 would be

50 to policy 1 (a)
250 to policy 2 (b)

by solving the simultainous equations
a+b=300
a+(1/5)b=100

could be over-simplifying things though.

 

[Mike375]

Yes, the object is to pay the maximum to Policy 2 but where the benefit of Policy 1 added to Policy 2 will still be $100,000

It is easy to do on the computer.

If the person wants the $100,000 and has $300 to spend then the premium for $100,000 is taken on Policy 1, which in this is case is $100 and so $200 remains. The $200 is applied to Policy 2 and buys $40,000.

Thus the $100,000 for Policy 1 can be reduced to $60,000 which means $40 becomes available and is applied to policy 2 and so buys and additional $8000 ands thus Policy 1 can be reduced by another $8000 and so on down the line. As a side not 5 cycles give a 99.98% result. That is, the addition of the premium for the two benefits is 99.98% of the 500. It takes about another 24 or 25 cycles to get from 99.98% to 100%.

Although it is 40 years ago I am sure I remember from high school that calculus is needed.

 

[Mike375]

sounds like compound interest to me...

not quite sure i get it though... for policy 1) you pay a premium of $100, what is the benefit paid out?

and for 2) what is the savings part? how is the benefit calculated?

How the policy pays does not matter. The same thing can be applied to many things.

Let's use wine as an example

From one container the wine is $10 per litre and from the other container the wine is $50 per litre. The 5 to 1 ratio is irrelevant.

You must buy 1 litre, no more, no less. One man only has $10 so he gets 1 litre from the cheap container. Another man has $50 so he gets his 1 litre from the expensive container.

A third man has $30. To make up his litre how much comes from the cheap container and how much from the expensive container

 

[cuteswan]

With some rusty algebra I came up with the following formulas:

Qe = (B - Pc) / (Pe - Pc)
then Qc = 1 - Qe

Where:
Qc = Quantity of cheap, as a fraction
Qe = Quantity of expensive to purchase, as a fraction

Inputs:
B = the budget to completely spend ($30 for wine)
Pc = Price of cheap per total Quantity ($10)
Pe = Price of expensive per total Quantity ($50)

Given:
Qc + Qe = 1, the total Quantity to be purchased with the budget (the "unit," or litres in the case of wine)
Pc ≤ b ≤ Pe, otherwise you buy only the expensive or go without

In the end, (Qe * Pe) + (Qc * Pc) = B, unless I messed up big-time.

Fortunately, you gave example numbers that came out to make the answer one-half for each type of wine or insurance. However, for my situation I'd just buy the plain term coverage and invest the difference in mutual funds, and you can probably guess what I'd do with the wine budget, too.

 

[Mike375]

cuteswan

Thanks for that.

Here is a solution just posted on an Australian guns/hunting forum. Both yours and his are making me giddy

A= spend 1 (ie cheap wine)
B= spend 2(exy wine)
x= quantity 1 (cheap wine)
y= quantity 2
z= y/x
C= total money available (ie A+B $30 in the wine case)
D= total quantity (in wine scenario 1l)

Ax + By = D, A + B = C

x(A + Bz) = D, B = C - A

x(A + Cz -Az) = D

D/x = A(1 - z) + Cz

(D/x - Cz)/(1-z) = A, B = C - A

hope this helps.

 

[Pauldohert]

They paid 25 for the drinks + 2 which the waiter kept so thats 27 which is 9 each?

I'd be more worried about the price of the drinks than the missing $. Move on to the next bar!

 

[cuteswan]

Okay, I made this workbook ( View attachment wine_and_insurance_worksheets.zip ) so I could double-check my answer, and it seems to work. However, both my answer above and the first worksheet may not be entirely clear because I tried to follow first example's numbers ("total cost for entire quantity using only the expensive option," etc.) instead of breaking it up by cost per unit; that's why there's a second worksheet.

Hopefully, the example formulas and numbers will explain it better. Then again, maybe I'm just getting carried away with logical stuff to distract myself from life's problems, which is why I started playing with MS Access again in the first place. (Also, I want to make people think I'm smart before asking lots of weird, esoteric questions about queries and data types. )

3 guys are hanging out together and walk into a bar and order 3 drinks. The waiter brings the drinks and tells them it will be $30 so they each put $10 in the middle of the table. The waiter brings the $30 to the bar and the bartender informs him that it is Happy Hour so he should have only charged $25. So the waiter heads back to the three guys with the $5 change. On his way he decides that dividing $5 between 3 guys is a hassle AND he didnt get a tip so he figures that he will pocket $2 and give each of the guys $1 back.

So here is the math part.
The 3 guys paid $30 and got a refund of $1 so each guy paid $9 for their drinks and the waiter pocketed $2
3 x 9 = 27 + 2 = 29
Where is the missing $1?

My father told me that one when I was about ten. I used marbles or cards or something to play it out, but when I explained the flaw to him he got mad and hit me for being a wise ass. So now I just say the dollar paid the taxes.

 

[ajetrumpet]

The 3 guys paid $30 and got a refund of $1 so each guy paid $9 for their drinks and the waiter pocketed $2
3 x 9 = 27 + 2 = 29
Where is the missing $1?

There is no missing dollar. If you would have spoken in the logical manner that events occured instead of shuffling them around in your mind, there would be no missing dollar. This is an OLD, OLD puzzle!

**$25 actual cost / 3 guys = $8.33 per drink.
**$8.33 per drink + $.67 tip (each drinker's share of the total tip) = $9
**$9 new price per drink + $1 (refund to each drinker)
**$10 x 3 drinkers = $30.

Take THAT, Fifty!!

 

[statsman]

I just assume the extra dollar went for tax.

 

[priji]

how do you find the roots (factors) of an algebraic cubic equation?

 

[priji]

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form
z^3+a_2z^2+a_1z+a_0==0
(1)

(the coefficient a_3 of z^3 may be taken as 1 without loss of generality by dividing the entire equation through by a_3). Mathematica can solve cubic equations exactly using the built-in command Solve[a3 x^3 + a2 x^2 + a1 x + a0 == 0, x]. The solution can also be expressed in terms of Mathematica algebraic root objects by first issuing SetOptions[Roots, Cubics->False].

The solution to the cubic (as well as the quartic) was published by Gerolamo Cardano (1501-1576) in his treatise Ars Magna. However, Cardano was not the original discoverer of either of these results. The hint for the cubic had been provided by Niccolò Tartaglia, while the quartic had been solved by Ludovico Ferrari. However, Tartaglia himself had probably caught wind of the solution from another source. The solution was apparently first arrived at by a little-remembered professor of mathematics at the University of Bologna by the name of Scipione del Ferro (ca. 1465-1526). While del Ferro did not publish his solution, he disclosed it to his student Antonio Maria Fior (Boyer and Merzbach 1991, p. 283). This is apparently where Tartaglia learned of the solution around 1541.

 

[ajetrumpet]

how do you find the roots (factors) of an algebraic cubic equation?

Provide a hand-written solution to the following problem, showing LESS than 30 lines of mathematical computation:

a + b + (c * d) - (e * f) + g = 40