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 U(m) 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