Annuity problem solving for i (interest rate)
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:
=\frac{1-v^{20}}{i})
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
Re: Annuity problem solving for i (interest rate)
your approach with the quadratic formula is valid (i haven't checked your working though)
Re: Annuity problem solving for i (interest rate)
Quote:
Originally Posted by
downthesun01 
From here multiply both sides by i and get:
OK; that simplifies to:
2v^20 - 3v^10 + 1 = 0
Let x = v^10; then:
2x^2 - 3x + 1 = 0; solve to get x = 1 or x = 1/2 ; reject x = 1.
So v^10 = 1/2
(1 / (1 + i))^10 = 1/2
1 / (1 + i) = (1/2)^(1/10)
Solve for i ; OK?
