i have two question in some assessments, both based on "Equations of Value Unknown interest rate" and two irregular contributions.
I've been over the textbook, and looking along time on line found very little. the problems are such that person x deposits a given amount now. (time zero?). and then another deposits at a different time different amount (example 1 year, and after 2 years its then given as FV to given amount.). the other one is like now given amount x is deposited, and 5 years given amount y is deposited then after 10 years is FV is such and such. what is the effective interest rate? (x an y are given in my question the point is i trying to understand the process.) and you cant use the simpler total of the two pv/fv etc. my understanding is some kind of polynomial is created
710t^0 + 570t^5 = 3520t^10 ?
and like
500t^0 + 525t^1 = 1175t^2
or should time zero be the future value?
You make up an equation. Assuming annual interest compounding, deposit $x$ for $10$ years and $y$ for $5$ years and have $S$ as a future value: $$x(1+r)^10+y(1+r)^5=S.$$ Given $x,y,S$, it is an equation with one unknown $r$, the interest rate.