I'm looking at this recurrence relation problem regarding interest that is compounded monthly. Basically, you deposit $1,000$ into a 5% interest bank account that is compounded monthly. So, after 2 months your account has $1,008.35. It asks you to set up a recurrence relation for the amount of money x(t+1), given that we know the amount of money in the account after t time steps x(t).
Here is my question: What do they mean by the amount of money x(t+1)? What is this supposed to represent in the equation? I thought I would be using x(t-1), which makes more sense to me. I'm not really sure what x(t+1) is supposed to be referring term in terms of the recurrence relation.
It's just shifting the relation one step along. So instead of saying "Given x(t-1), write an expression for x(t)", it's saying "Given x(t), write an expression for x(t+1)". Equivalently, instead of "Given the balance last month, work out an expression for the balance this month" it's asking "Given the balance this month, work out an expression for the balance next month".