Thread: 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:



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

your approach with the quadratic formula is valid (i haven't checked your working though)

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?