your approach with the quadratic formula is valid (i haven't checked your working though)
The present value of a 10-year annuity-immediate with level annual payments and interest rate i is x. The present value of a 20-year annuity-immediate with the same payment and interest rate is 1.5x. Find i.
So far I have:
where
So:
From here multiply both sides by i and get:
From here I'm not sure what to to do.
I know that
I was thinking that I could substitute and to setup and solve quadratic formula.
Doing so gives x=0.5,1
Therefore
But I'm not sure that's a proper way of solving the problem. Thanks