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# Struggling with Mathematical Modelling watch

1. I am REALLY struggling with Mathematical Modelling and I am a little bit nervous now as it is so close to the exam period. I just never know what they are looking for. With other types of maths, you can pick up terminology and you know what you are being asked, e.g. if they ask you to work out gradient, you differentiate.

With this modelling, I don't know when to use the difference equations, when to use normal differential equations, etc.

What is the best method to revise this topic? I can't even seem to do one or two questions because I actually have no clue what they are asking me to do.

For example (bold letters in brackets are supposed to be subscripts):

At the end of the m'th year, a borrower owes £U(m) to a building society for the mortgage of his house, where U(m) satisfies:

U(m) = 1.06U(m-1) - 7200 pounds.

What is the interest rate charged by the building society and how much does he repay each year?
What is the equilibrium solution N, of this equation?
If the house initially cost £90,000, calculate how long it will take to pay off the mortgage, and the total amount the borrower will pay?

I thought the interest was 1.06%, but it is actually 6%. Why is this?

The amount he pays back I said was £7,200, which is correct.

For the equilibrium, I thought you had to differentiate and the equilibrium is when the differential equals 0, but in the answers, they did N = 1.06N -7200, and then solved it (and got 120 000). Why did they do this and how can they just swap U(m-1) for N, if Um is N? What exactly is the "equilibrium"?

I didn't have a clue how to work out the last bit. The answer said that somehow the difference from the equilibrium (90 000 - 120 000) satisfies the equation x(m) = (1.06)^m *x(0). How?

Sorry if this is a lot but I haven't got a clue how to do these types of questions which is why I posted this. Thank you for any help
2. It is the previous amount times by 1.06.
(Multiple-1)*100 = Interest

I'm afraid I'm not familiar with the last two questions. However, by the answer giving it seems as if they are asking for when the repayments are the same. This is what you described by saying that the differential is 0, perhaps someone could clarify on that.
3. Bump.
4. No help at all?
5. (Original post by claret_n_blue)
At the end of the m'th year, a borrower owes £U(m) to a building society for the mortgage of his house, where U(m) satisfies:

U(m) = 1.06U(m-1) - 7200 pounds.

What is the interest rate charged by the building society and how much does he repay each year?
What is the equilibrium solution N, of this equation?

I thought the interest was 1.06%, but it is actually 6%. Why is this?
the equilibrium position is where the amount owed does not change from one year to the next.
if we call this amount A

then A = 1.06A - 7200

if you multiply an amount by 1.06 you are increasing it by 6 %... so that is the interest rate.

the bear

6. (Original post by the bear)
the equilibrium position is where the amount owed does not change from one year to the next.
if we call this amount A

then A = 1.06A - 7200

if you multiply an amount by 1.06 you are increasing it by 6 %... so that is the interest rate.

the bear

So when do I have to differentiate?

Also, if I multiply an amount by 1.54, is that an increase of 54%. What if I had multiplied by simply 0.06, how much of an increase would that be? 0.6%?
7. if you multiply by 0.06 the amount will decrease by 94%

the bear

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